On the mod-2 cohomology of SL3(Z[1/2, i])

被引：0

作者：

Henn, Hans -Werner ^{[1
]}

机构：

[1] Univ Strasbourg, Inst Rech Math Avancee, CNRS, Strasbourg, France

来源：

TUNISIAN JOURNAL OF MATHEMATICS | 2019年 / 1卷 / 04期

关键词：

cohomology of special and general linear groups; Quillen conjecture; LINEAR-GROUPS; CONSTRUCTION; SUBGROUPS;

D O I：

10.2140/tunis.2019.1.539

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let gamma = SL3(Z[1/2, i]), let X be any mod-2 acyclic gamma-CW complex on which gamma acts with finite stabilizers and let X-s be the 2-singular locus of X. We calculate the mod-2 cohomology of the Borel construction of X-s with respect to the action of gamma. This cohomology coincides with the mod-2 cohomology of gamma in cohomological degrees bigger than 8 and the result is compatible with a conjecture of Quillen which predicts the structure of the cohomology ring H*(gamma; F-2).

引用

页码：539 / +

页数：25

共 50 条

[31] EXOTIC CLASSES IN THE MOD 2 COHOMOLOGY OF GL(n)(Z[1/2])
Henn, Hans-Werner
Lannes, Jean
ENSEIGNEMENT MATHEMATIQUE, 2008, 54 (1-2): : 111 - 112
[32] Hochschild cohomology ring of the mod-2 group ring of the generalized quaternion group
Hayami, Takao
COMMUNICATIONS IN ALGEBRA, 2006, 34 (11) : 3985 - 4005
[33] Product theorems in SL2 and SL3
Chang, Mei-Chu
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2008, 7 (01) : 1 - 25
[34] ON COHOMOLOGY OF MOD-2 STEENROD ALGEBRA AND NON-EXISTENCE OF ELEMENTS OF HOPF INVARIANT 1
WANG, JSP
ILLINOIS JOURNAL OF MATHEMATICS, 1967, 11 (03) : 480 - &
[35] Cohomology of simple modules for sl3 (k) in characteristic 3
Ibrayeva, A. A.
Ibraev, Sh Sh
Yeshmurat, G. K.
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021, 103 (03): : 36 - 43
[36] The mod-2 cohomology ring of the third Conway group is Cohen-Macaulay
King, Simon A.
Green, David J.
Ellis, Graham
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2011, 11 (02): : 719 - 734
[37] ON THE HOPF ALGEBRA STRUCTURE OF THE MOD-2 COHOMOLOGY OF A FINITE H-SPACE
LIN, J
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1984, 20 (04) : 877 - 892
[38] THE ROLE OF THE STEENROD ALGEBRA IN THE MOD-2 COHOMOLOGY OF A FINITE H-SPACE
LIN, JP
ANNALS OF MATHEMATICS STUDIES, 1987, (113): : 206 - 227
[39] THE MOD-2 COHOMOLOGY ALGEBRAS OF FINITE-GROUPS WITH SEMIDIHEDRAL SYLOW 2-SUBGROUPS
SASAKI, H
COMMUNICATIONS IN ALGEBRA, 1994, 22 (11) : 4123 - 4156
[40] MOD-2 COHOMOLOGY RINGS OF EXTRA-SPECIAL 2-GROUPS AND SPINOR GROUPS
QUILLEN, D
MATHEMATISCHE ANNALEN, 1971, 194 (03) : 197 - &

← 1 2 3 4 5 →