Cohomology of classifying spaces of loop groups and finite Chevalley groups associated with spin groups

Masaki Kameko

doi:10.1016/j.topol.2015.05.031

Cohomology of classifying spaces of loop groups and finite Chevalley groups associated with spin groups

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

Abstract

Let q be a power of an odd prime p and F_q be the finite field with q elements. For n≥3, we prove the mod 2 cohomology of the finite Chevalley group Spin_n(F_q) is isomorphic to that of the classifying space of the loop group of the spin group Spin(n).

Original language	English
Pages (from-to)	522-536
Number of pages	15
Journal	Topology and its Applications
Volume	196
DOIs	https://doi.org/10.1016/j.topol.2015.05.031
Publication status	Published - 2015 Dec

Keywords

Classifying space
Cohomology
Finite Chevalley group
Free loop space
Loop group

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2015.05.031

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title = "Cohomology of classifying spaces of loop groups and finite Chevalley groups associated with spin groups",

abstract = "Let q be a power of an odd prime p and Fq be the finite field with q elements. For n≥3, we prove the mod 2 cohomology of the finite Chevalley group Spinn(Fq) is isomorphic to that of the classifying space of the loop group of the spin group Spin(n).",

keywords = "Classifying space, Cohomology, Finite Chevalley group, Free loop space, Loop group",

author = "Masaki Kameko",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

year = "2015",

month = dec,

doi = "10.1016/j.topol.2015.05.031",

language = "English",

volume = "196",

pages = "522--536",

journal = "Topology and its Applications",

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AU - Kameko, Masaki

PY - 2015/12

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N2 - Let q be a power of an odd prime p and Fq be the finite field with q elements. For n≥3, we prove the mod 2 cohomology of the finite Chevalley group Spinn(Fq) is isomorphic to that of the classifying space of the loop group of the spin group Spin(n).

AB - Let q be a power of an odd prime p and Fq be the finite field with q elements. For n≥3, we prove the mod 2 cohomology of the finite Chevalley group Spinn(Fq) is isomorphic to that of the classifying space of the loop group of the spin group Spin(n).

KW - Classifying space

KW - Cohomology

KW - Finite Chevalley group

KW - Free loop space

KW - Loop group

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VL - 196

SP - 522

EP - 536

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Cohomology of classifying spaces of loop groups and finite Chevalley groups associated with spin groups

Abstract

Keywords

ASJC Scopus subject areas

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