Cohomology of toroidal orbifold quotients

Alejandro Adem; Ali Nabi Duman; José Manuel Gómez

doi:10.1016/j.jalgebra.2011.08.004

Cohomology of toroidal orbifold quotients

Alejandro Adem^*, Ali Nabi Duman, José Manuel Gómez

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let φ:Z/p→GL_n(Z) denote an integral representation of the cyclic group of prime order p. This induces a Z/p-action on the torus X=Rⁿ/Zⁿ. The goal of this paper is to explicitly compute the cohomology groups H*(X/Z/p;Z) for any such representation. As a consequence we obtain an explicit calculation of the integral cohomology of the classifying space associated to the family of finite subgroups for any crystallographic group Γ=Zⁿ⋊ Z/p with prime holonomy.

Original language	English
Pages (from-to)	114-136
Number of pages	23
Journal	Journal of Algebra
Volume	344
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.08.004
State	Published - 15 Oct 2011
Externally published	Yes

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (A. Adem), [email protected] (A.N. Duman), [email protected] (J.M. Gómez). 1 Partially supported by NSERC.

Keywords

Crystallographic groups
Group cohomology
Serre spectral sequence
Toroidal orbifolds

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2011.08.004

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title = "Cohomology of toroidal orbifold quotients",

abstract = "Let φ:Z/p→GLn(Z) denote an integral representation of the cyclic group of prime order p. This induces a Z/p-action on the torus X=Rn/Zn. The goal of this paper is to explicitly compute the cohomology groups H*(X/Z/p;Z) for any such representation. As a consequence we obtain an explicit calculation of the integral cohomology of the classifying space associated to the family of finite subgroups for any crystallographic group Γ=Zn⋊ Z/p with prime holonomy.",

keywords = "Crystallographic groups, Group cohomology, Serre spectral sequence, Toroidal orbifolds",

author = "Alejandro Adem and Duman, \{Ali Nabi\} and G{\'o}mez, \{Jos{\'e} Manuel\}",

note = "Funding Information: E-mail addresses: [email protected] (A. Adem), [email protected] (A.N. Duman), [email protected] (J.M. G{\'o}mez). 1 Partially supported by NSERC.",

year = "2011",

month = oct,

day = "15",

doi = "10.1016/j.jalgebra.2011.08.004",

language = "English",

volume = "344",

pages = "114--136",

journal = "Journal of Algebra",

issn = "0021-8693",

number = "1",

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T1 - Cohomology of toroidal orbifold quotients

AU - Adem, Alejandro

AU - Duman, Ali Nabi

AU - Gómez, José Manuel

N1 - Funding Information: E-mail addresses: [email protected] (A. Adem), [email protected] (A.N. Duman), [email protected] (J.M. Gómez). 1 Partially supported by NSERC.

PY - 2011/10/15

Y1 - 2011/10/15

N2 - Let φ:Z/p→GLn(Z) denote an integral representation of the cyclic group of prime order p. This induces a Z/p-action on the torus X=Rn/Zn. The goal of this paper is to explicitly compute the cohomology groups H*(X/Z/p;Z) for any such representation. As a consequence we obtain an explicit calculation of the integral cohomology of the classifying space associated to the family of finite subgroups for any crystallographic group Γ=Zn⋊ Z/p with prime holonomy.

AB - Let φ:Z/p→GLn(Z) denote an integral representation of the cyclic group of prime order p. This induces a Z/p-action on the torus X=Rn/Zn. The goal of this paper is to explicitly compute the cohomology groups H*(X/Z/p;Z) for any such representation. As a consequence we obtain an explicit calculation of the integral cohomology of the classifying space associated to the family of finite subgroups for any crystallographic group Γ=Zn⋊ Z/p with prime holonomy.

KW - Crystallographic groups

KW - Group cohomology

KW - Serre spectral sequence

KW - Toroidal orbifolds

UR - https://www.scopus.com/pages/publications/80052266212

U2 - 10.1016/j.jalgebra.2011.08.004

DO - 10.1016/j.jalgebra.2011.08.004

M3 - Article

AN - SCOPUS:80052266212

SN - 0021-8693

VL - 344

SP - 114

EP - 136

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Cohomology of toroidal orbifold quotients

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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