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...egensburg Surgery Blockseminar 2012: Program#Poincaré complexes|Poincaré complexes]]: \cite{Lück2001}[3.1] L; [[User:Freiburg|Freiburg]], [[Media:Regensburg2
8 KB (1,111 words) - 15:44, 9 May 2012
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Two aspherical $CW$-complexes are homotopy equivalent if and only if their fundamental groups are isomorp
... groups bijections. Hence it suffices to construct for two aspherical $CW$-complexes $X$ and $Y$ together with an isomorphism $\phi \colon \pi_1(X) \to \pi_1(Y)
59 KB (7,971 words) - 14:39, 27 September 2012
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...sifies higher-dimensional manifolds. (The statement in terms of Poincar\'e complexes is given e.g. in \cite{Wall1999}.)
34 KB (5,424 words) - 07:01, 6 November 2021
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... homotopy classes of self-maps and so the corresponding rational Poincaré complexes are inflexible. They also indicate why the algebras $\mathcal{M}_1$ and $\m
4 KB (558 words) - 11:19, 10 June 2010
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However, the definition of a cup product generalizes to complexes (and so to topological manifolds).
This is an advantage for mathematicians who are interested in complexes and topological manifolds (not only in PL and smooth manifolds). See \cite[
14 KB (2,390 words) - 10:32, 16 December 2023
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<!-- *[[Poincaré complexes]] -->
4 KB (592 words) - 15:25, 18 April 2012
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...-history.mcs.st-and.ac.uk/Biographies/Poincare.html Poincaré] || {{citeD2|Poincaré1899|Complément à l'Analysis situs.}}
... Lefschetz] || {{citeD2|Lefschetz1926|Intersections and transformations of complexes and manifolds}}
10 KB (1,227 words) - 15:06, 18 May 2014
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== Poincaré complexes ==
8 KB (1,194 words) - 15:42, 9 May 2012
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... Surgery Seminar 2012: Program#Structured chain complexes|Structured chain complexes]] [[User:Ranicki|AR]] [http://www.dailymotion.com/video/xr7mn5_mfo8_tech vi
...and L-groups via chain complexes|Algebraic surgery and L-groups via chain complexes]] [[User:Ranicki|AR]] [http://www.dailymotion.com/video/xr7zrd_mfo10_tech
8 KB (1,000 words) - 09:47, 6 August 2012
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# [[Reducible Poincaré Complexes (Ex)]]
# [[Forms and chain complexes I (Ex)]]
3 KB (328 words) - 22:51, 9 June 2012
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...neral this is most easily seen in the more abstract setting of [[Poincaré complexes]], see \cite{Lück2001|Section 3.1}.
Let $(X,[X],w)$ and $(X',[X'],w')$ be connected Poincaré complexes and $f:X\rightarrow X'$ be a homotopy equivalence. Then $(X,[X],w'\circ f_*
9 KB (1,506 words) - 08:24, 14 April 2014
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Exercises: [[K-group, zeroth (Ex)]], [[Finitely dominated CW complexes (Ex)]]
...e the Whitehead torsion of a homotopy equivalence of finite connected $CW$-complexes.
17 KB (2,410 words) - 15:27, 29 August 2013
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... used to extend the definition of the Stiefel-Whitney classes to Poincaré complexes.
8 KB (1,305 words) - 02:11, 3 February 2021
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... '''$\textup{CW}_0$''' be the category of reduced CW-complexes, that is CW-complexes with $0$-skeleton a point which is the base-point, and base-point preservin
...D}^n$-complexes and oriented or ''degree $1$'' morphisms of ${\rm PD}^n$—complexes.<br>
9 KB (1,565 words) - 14:29, 22 July 2014
