Questions tagged [examples]
For questions requesting examples of a certain structure or phenomenon
538
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Examples of a topological semidirect product
Let $G$ be a compact topological group, and $\operatorname{Aut}(G)$ the group of autohomeomorphisms of $G$. I have proved some (topological) results about the holomorph $G\leftthreetimes \operatorname{...
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Examples of value quantales
In his paper "Quantales and continuity spaces" R. C. Flagg gives the following examples of value quantales: the lattice $\bf{2}$ of truth values with usual addition, the lattice $\mathbb{R}_{+}$ of ...
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Is a successor to a successor to the trivial group topology on an Abelian group, totally bounded?
Is there an example of an Abelian group $G$ and group topologies $\cal S$ and $\cal T$ on it such that $\cal S$ is an immediate successor to the trivial topology on $G$ (i.e there is no other group ...
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Roller's problem on median groups
At the end of his dissertation Poc Sets, Median Algebras and Group Actions, Martin Roller asks
A group $G$ is called median if it acts freely and transitively on a median algebra. This is ...
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3
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Can integration spoil real-analyticity?
Is there an example of a function $f:(a,b)\times(c,d)\to\mathbb{R}$, which is real analytic in its domain, integrable in the second variable, and such that the function
$$ g:(a,b)\to\mathbb{R},\qquad ...
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Examples of (non-normal) unibranched rings?
For a local integral domain $R$ the following are equivalent:
a) The integral closure of $R$ in its fraction field (i.e., the normalization of $R$) is again local.
b) The henselization of $R$ is ...
user78294
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Example of a triangulable topological manifold which does not admit a PL structure
I know there are some examples of manifolds which don't admit a PL structure (combinatorial triangulation), and that it has been recently proven that in dimension $n\geq5$ there are manifold which are ...
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system with solutions $\{x-a:0\leqslant a\leqslant z-1\}$ [closed]
What must be $F$ there where $0=F(1,x,0)=F(x-0,x,z)=F(x-1,x,z)=F(x-2,x,z)=F(x-3,x,z)=$ $\dots$ $=f(x-z-1,x,z)=0$?
Define $F$ in the domain where a continuous function exists that behaves so for $x\...
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Linear vs smooth actions of finite groups on spheres, euclidean spaces and closed disks
I would like to know examples (with references, if possible) of the following:
(1) a finite group $G$ acting effectively and smoothly on a sphere $S^n$ (any $n$) but admitting no effective linear ...
2
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1
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Images of interval edge coloring
I found out the definition of interval edge colorings, concept put by Kamalian in various papers but could not find a graph depicting an example. Where can I find pictures of explicit examples of ...
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Non-field example of a commutative, local, dual ring with nilradical $N$ such that $ann(N)\nsubseteq N$
I asked this question on math.stackexchange a month ago with no progress, even after a bounty. I hope to eliminate one if the other receives a satisfactory answer.
For an ideal $I\lhd R$ in a ...
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Example of a torsionfree group satisfying a cohomological condition
Let us call a finitely generated group $G$ cohomologically rich if for each $k \geq 0$, we can find a subgroup $G'$ and a prime $p$ such that $H^k(G';\mathbb F_p) \neq 0$. Examples which come to mind ...
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Examples of TVS with no non-trivial open convex subsets
I give here the classical example of the space $E = L^p([0,1])$ which has no open convex subsets apart from $\emptyset$ and $E$. Consequently, there is no non-trivial continuous linear form on $E$.
...
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Variation of Hodge structures associated to a hermitian symmetric domain
Let $D$ be an irreducible hermitian symmetric domain. Then there exists a variation of Hodge structures $(h_s)_{s\in D}$ on a vector space $V$ satisfying specific conditions which depend on $D$ such ...
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Example s.t. the unbased loop-space is not $\Omega X \times X$
For a connected pointed CW-complex $X$, let us write (as usual) $\Omega X$ for the space of based loops at $X$. I am looking for an example where the space $\Omega' X$ of all (unbased) loops in $X$ is ...
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Bialgebras with Hopf restricted (or Sweedler) duals
It is known from the general theory that, given a bialgebra (over a field $k$)
\begin{equation}
\mathcal{B}=(B,\mu,1_B,\Delta,\epsilon)
\end{equation}
the Sweedler's dual $\mathcal{B}^0$ (called also ...
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Need examples of homotopy orbit and fixed points
I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or ...
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A Hausdorff atom in lattice of group topologies
Do you have an example of an infinite Hausdorff nonabelian topological group $(G,\mathcal T)$ such that for any nontrivial group topology $\mathcal S$ on $G$ with $\mathcal S\subseteq \mathcal T$ we ...
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An example of two cofibrant dg categories whose tensor product is not cofibrant
I have been reading the paper by Toën "The homotopy theory of dg categories and derived Morita theory" where in chapter 4 it is stated that the tensor product of two cofibrant dg categories $C$ and $D$...
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An example of a simple infinite 2-group
I've asked this question before on Mathematics, and they suggested me to ask here (Link).
Is there an example of a simple infinite $2$-group?
Informations
If a $2$-group is Artinian I know that it ...
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Looking for interesting, natural models of this algebraic theory in which $x^\dagger$ is not always the multiplicative inverse of $x$
It is easy to think up interesting, natural models of the algebraic theory presented as follows, such that in these models, $x^\dagger$ is always the multiplicative inverse of $x$.
Question. What ...
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Example of a polycyclic group which is not of polynomial growth? [closed]
The title already says everything: What is an example of a polycyclic group $G$ which is not of polynomial growth (equivalently, by Gromov's theorem, which is not virtually nilpotent)?
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Divergence invariant lifting of a vector field via a submersion
What is an example of a smooth submersion $P:S^{3}\to S^{2}$ for which the following statment is Not true:
For every vector field $X$ on $S^{2}$ there is a non vanishing vector field $\tilde{X}$...
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Is Hironaka's example the only known deformation of Kähler manifolds with non-Kähler central fibre?
A well-known example in the deformation theory of compact complex manifolds is the one given by Hironaka in his 1962 paper An Example of a Non-Kählerian Complex-Analytic Deformation of Kählerian ...
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Examples of compact complex non-Kähler manifolds which satisfy $h^{p,q} = h^{q,p}$
The existence of a Kähler metric on a compact complex manifold $X$ imposes restrictions on it's Dolbeault cohomology; namely, $h^{p,q}(X) = h^{q,p}(X)$ for every $p$ and $q$. I am looking for some ...
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Recent, elementary results in algebraic geometry
Next semester I will be teaching an introductory algebraic geometry class for a smallish group of undergrads. In the last couple weeks, I hope that each student will give a one-hour presentation. ...
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Existence of orientation preserving, finite order self homeomorphism on a genus 2 surface without fixed point
Let $M$ be a compact 2-manifold of genus 2. Does there exist an orientation preserving homeomorphism $f:M\to M$, so that $f^n=id$ for some integer $n$, and $f$ doesn't have fixed points?
Using ...
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Examples of unproven but likely true existential sentence (in the sense of incompleteness)
Some examples of universal statements that are unproven but likely true include the Riemann hypothesis (all non-trivial zeros of the zeta function have real part 1/2) and the Goldbach conjecture (all ...
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Is there a smooth rationally connected, proper variety $M$ over $\mathbb{C}$ such that c_1(L)([A]) = 1 which is not projective space?
Is there a smooth, rationally connected, projective variety $M$, which is not a projective space and is equipped with an ample line bundle $L$, such that the homology class of the curves $[A]$ which ...
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Examples of functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition
there are examples of lacunary functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition.I want to know more examples of those functions,the more the better,...
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Example of a specific manifold
I want to find a example of a manifold that has positive scalar curvature but is not half conformally flat.
Does there exists such manifolds?
Thanks.
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Examples of nontrivial local systems in Decomposition Theorem
There is a proper map $f: X \rightarrow Y$ of projective varieties. The Decomposition Theorem of Beilinson–Bernstein–Deligne-Gabber states that
$$Rf∗IC_X \cong \oplus_a IC_{\bar{Y_a}}(L_a)[shifts]$...
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Mumford-Ramanujam examples in characteristic p [and in Arakelov geometry]
For a compact Riemann surface $B$ of genus $\geq 2$, it is a consequence of the Narasimhan-Seshadri theorem that there exist rank-$2$ vector bundles $E \to B$ of degree zero, all of whose symmetric ...
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How weird can Modular Tensor Categories be over non-algebraically closed fields?
I am trying to understand better the behaviour and character of modular tensor categories over non-algebraically closed fields. How weird can they be?
The reason I am interested in this is that my ...
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Are all vector-space valued functors on sets free?
Let $\mathbf{Set}$ be the category of finite sets and functions between them, and let $\mathbf{Vect}$ be the category of finite-dimensional complex vector spaces and linear transformations between ...
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A sequence of subsets of an infinite group
Is there an infinite group $G$ such that there is not any sequence $(A_n)$ of its subsets such that always
$$A_n=A_n^{-1}, \quad A_{n+1}A_{n+1}\subsetneqq A_n$$
?
link
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smooth affine surfaces over algebraically closed fields with trivial l-torsion of the Brauer group
I am looking for examples of smooth affine surfaces over algebraically closed fields with trivial $\ell$-torsion of the Brauer group.
Related questions: Schemes with trivial brauer group and Brauer ...
user19475
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Example(s) of monoidal symmetric closed category with NNO without infinite coproducts?
The question is in the title, here is my motivation:
$\require{AMScd}$Let $(\mathcal C,\otimes,I)$ be a monoidal symmetric closed category. Then, the tensor product commutes with colimits, and if $\...
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Closed 4-manifolds with uncountably many differentiable structures
I know that $\mathbb{R}^4$ admits uncountably many differentiable structures and I was wandering what happen if we consider closed 4-manifolds. Are there any closed 4-manifolds with uncountably many ...
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Homeomorphisms of product spaces: an example
In the first of these lectures (http://www.mpim-bonn.mpg.de/node/4436) given by M. Freedman he says that there exists (compact metric) spaces $X$ and $Y$ such that $X\times S^{1}$ is homeomorphic to $...
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Do you have examples of such "transitive" elements?
(I've asked the same question at the MSE, so far with no answers, so I thought I'd try it here as well. If there's some clash with any site rules, please let me know and I'll abide.)
Let $A$ be a set ...
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Unravelling some hypotheses on a variety
In Le group de Brauer II, Grothendieck states
Proposition 1.4.- Soit $X$ a préschéma noetherien. Supposon que les anneaux hensélisés stricts des anneaux locaux de $X$ soient factoriels, [...] Alors ...
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Mistakes in mathematics, false illusions about conjectures
Since long time ago I have been thinking in two problems that I have not been able to solve. It seems that one of them was recently solved. I have been thinking a lot about the motivation and its ...
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A model with $\kappa$ many automorphism and a rigid element.
The following should be known, but I could not find an example.
Let $\kappa$ be an uncountable cardinal. Find a model $M$ of size $\kappa$ which has $\ge\kappa$ many automorphisms, but for some $m\in ...
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Simple but topologizable [closed]
Do you have an example of an infinite simple group with at least 3 distinct group topologies on it?
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Examples of groups such that order isomorphism of the subgroups of $G\times G$ and $H\times H$ does not imply isomorphism of $G$ and $H$
Let $G$ and $H$ be groups, $\operatorname{Sub}(G\times G)$ be the set of all subgroups of $G\times G$ and $\operatorname{Sub}(H\times H)$ be the set of all subgroups of $H\times H$. Assume there ...
- 1,145
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Measures which exhibit the "uncorrelated implies independent" property
Let $X$ be a topological linear space, and let $X^*$ be its dual space. Suppose that $X$ is complete and Hausdorff, and $X^*$ separates points. Let $Y$ be another such space, and let $f : X \to Y$ be ...
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Nontrivial upper bounds on proof-theoretic ordinals of strong theories: do we have any?
Motivated by Consistency of Analysis (second order arithmetic) and Proof-Theoretic Ordinal of ZFC or Consistent ZFC Extensions?, I have the following question:
Are there any examples of strong ...
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3
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Fibrations with isomorphic fibers, but not Zariski locally trivial
(I posted this same question on MSE. Sorry if it is too elementary.)
I am looking for examples of fibrations $f:X\to Y$ where the fibers are all isomorphic, but $f$ is not Zariski locally trivial. In ...
- 1,514
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Not quite adjoint functors
What are standard and/or natural examples of pairs of functors $F:C\leftrightarrows D:G$ and unnatural bijections $\hom_D(Fx,y)\to\hom_C(x,Gy)$ for all $x$ and $y$? Can one do this so that the ...
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