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Results tagged with gt.geometric-topology
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user 8032
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
2
votes
Ehresmann fibration theorem for manifolds with boundary
Let $D(M)$ be the boundary of $M \times [0,1]$ (by smoothing corners, this can be understood as smooth). Then $f: M \to N$ induces a smooth map
$$
D(f): D(M) \to D(N)\, .
$$
Further, $D(f)$ is a prop …
- 18.5k
7
votes
Homotopy groups of spaces of embeddings
Here are some comments:
1) Concerning finiteness results for spaces of embeddings, here is what I remember. The layers of the Goodwillie-Weiss tower when $M^m$ is closed and $N= \Bbb R^n$ have finit …
- 18.5k
2
votes
Accepted
Embedding spaces and surface knots in high dimensional manifolds
Here are some general comments. We can let $\Sigma$ be any closed smooth $k$-manifold and let $X$ be any smooth $n$-manifold.
Fix a basepoint embedding $\Sigma \to X$.
Let $N$ be a compact regular n …
- 18.5k
14
votes
Accepted
Characteristic classes for block bundles
I don't know where the results are written down in one place (perhaps in the book of Madsen and Milgram?), but see the the end of this post for a list of references.
In any case, here is a proof of …
- 18.5k
8
votes
contractible configuration spaces
I believe each of these arguments will work.
Argument 1: Consider $S^n \subset \Bbb R^{n+1} \subset S^{n+1}$, where the last inclusion is
given by the upper hemisphere (which is homeomorphic to $\Bbb …
- 18.5k
10
votes
classifying space of orthogonal groups
$BO$ can be defined as the colimit over $(k,n)$ of Grassmanians $G_k(\Bbb R^n)$ of $k$-dimensional linear subspaces of $\Bbb R^n$ (the limit over $n$ is defined by standard inclusions $\Bbb R^n \subse …
- 18.5k
14
votes
Unstable manifolds of a Morse function give a CW complex
(1). Some experts tell me that Laudenbach's paper is incomplete and contains gaps.
I will retract this for now. I do recall being told this, but I am not
aware at this point in time where the gaps …
- 18.5k