Constructing homotopy equivalences of chain complexes of free
ZG-modules

D 2014

Constructing homotopy equivalences of chain complexes of free ZG-modules

VOKŘÍNEK, Lukáš

Základní údaje

Originální název

Constructing homotopy equivalences of chain complexes of free ZG-modules

Autoři

VOKŘÍNEK, Lukáš

Vydání

Neuveden, An Alpine Expedition through Algebraic Topology, od s. 279-296, 18 s. 2014

Nakladatel

American Mathematical Soc.

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Odkazy

URL

Kód RIV

RIV/00216224:14310/14:00074505

Organizační jednotka

Přírodovědecká fakulta

ISBN

978-0-8218-9145-2

ISSN

UT WoS

000361077800015

Klíčová slova anglicky

chain complex; homotopy module; reduction; homotopy equivalence; transfer

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 26. 6. 2020 11:16, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

We describe a general method for algorithmic construction of G-equivariant chain homotopy equivalences from non-equivariant ones. As a consequence, we obtain an algorithm for computing equivariant (co)homology of Eilenberg-MacLane spaces K(pi,n), where pi is a finitely generated ZG-module. The results of this paper will be used in a forthcoming paper to construct equivariant Postnikov towers of simply connected spaces with free actions of a finite group $G$ and further to compute stable equivariant homotopy classes of maps between such spaces. The methods of this paper work for modules over any non-negatively graded differential graded algebra, whose underlying graded abelian group is free with 1 as one of the generators.

Návaznosti

GBP201/12/G028, projekt VaV

Název: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Investor: Grantová agentura ČR, Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Citovat

VOKŘÍNEK, Lukáš. Constructing homotopy equivalences of chain complexes of free ZG-modules. In Christian Ausoni, Kathryn Hess, Brenda Johnson, Wolfgang Lück, Jérôme Scherer. An Alpine Expedition through Algebraic Topology. Neuveden: American Mathematical Soc., 2014, s. 279-296. ISBN 978-0-8218-9145-2.

@inproceedings{1233007,
   author = {Vokřínek, Lukáš},
   address = {Neuveden},
   booktitle = {An Alpine Expedition through Algebraic Topology},
   editor = {Christian Ausoni, Kathryn Hess, Brenda Johnson, Wolfgang Lück, Jérôme Scherer},
   keywords = {chain complex; homotopy module; reduction; homotopy equivalence; transfer},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Neuveden},
   isbn = {978-0-8218-9145-2},
   pages = {279-296},
   publisher = {American Mathematical Soc.},
   title = {Constructing homotopy equivalences of chain complexes of free ZG-modules},
   url = {https://arxiv.org/pdf/1304.6771.pdf},
   year = {2014}
}

TY  - CONF
ID  - 1233007
AU  - Vokřínek, Lukáš
PY  - 2014
TI  - Constructing homotopy equivalences of chain complexes of free ZG-modules
PB  - American Mathematical Soc.
CY  - Neuveden
SN  - 9780821891452
KW  - chain complex
KW  - homotopy module
KW  - reduction
KW  - homotopy equivalence
KW  - transfer
UR  - https://arxiv.org/pdf/1304.6771.pdf
L2  - https://arxiv.org/pdf/1304.6771.pdf
N2  - We describe a general method for algorithmic construction of G-equivariant chain homotopy equivalences from non-equivariant ones. As a consequence, we obtain an algorithm for computing equivariant (co)homology of Eilenberg-MacLane spaces K(pi,n), where pi is a finitely generated ZG-module. The results of this paper will be used in a forthcoming paper to construct equivariant Postnikov towers of simply connected spaces with free actions of a finite group $G$ and further to compute stable equivariant homotopy classes of maps between such spaces. The methods of this paper work for modules over any non-negatively graded differential graded algebra, whose underlying graded abelian group is free with 1 as one of the generators.
ER  -

VOKŘÍNEK, Lukáš. Constructing homotopy equivalences of chain complexes of free ZG-modules. In Christian Ausoni, Kathryn Hess, Brenda Johnson, Wolfgang Lück, Jérôme Scherer. \textit{An Alpine Expedition through Algebraic Topology}. Neuveden: American Mathematical Soc., 2014, s.~279-296. ISBN~978-0-8218-9145-2.

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