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Results tagged with homological-algebra
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user 482329
(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
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Image of the boundary maps in the homological spectral sequence of a filtration of a chain c...
I'm trying to understand the construction of the homological spectral sequence of a filtration given in C.A.Weibel ''An introduction to homological algebra''. Here, they start with a filtration of a c …
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Infinite dimensional homology and spectral sequences
I am new to spectral sequences, so I'm not sure about the difficulty of this question.
Suppose we have a filtration of a chain complex $\emptyset=D_{-1}\subset D_{0}\subset D_1\subset\dots D_n= C$ and …
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Finiteness of $\ell^2$-Betti numbers
I'm reading the paper "Improved algebraic fibering" by Sam Fisher (https://arxiv.org/pdf/2112.00397.pdf) and in the proof of lemma 6.4 it claims the followng:
$(\mathcal{D}_{\mathbb{F}K}\ast\mathbb{Z} …
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