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On the Rothenberg–Steenrod spectral sequence for the mod 2 cohomology of classifying spaces of spinor groups

Masaki Kameko and Mamoru Mimura

Geometry & Topology Monographs 13 (2008) 261–279

DOI: 10.2140/gtm.2008.13.261

arXiv: 0904.0800
Abstract

We compute the cotorsion product of the mod 2 cohomology of spinor group spin(n), which is the E2–term of the Rothenberg–Steenrod spectral sequence for the mod 2 cohomology of the classifying space of the spinor group spin(n). As a consequence of this computation, we show the non-collapsing of the Rothenberg–Steenrod spectral sequence for n≥ 17.

Keywords

Steenrod square, classifying space, cohomology, Lie group, spectral sequence
Mathematical Subject Classification

Primary: 55R40

Secondary: 55T99
References
Publication

Received: 31 May 2006
Revised: 20 August 2007
Accepted: 27 August 2007
Published: 25 February 2008
Authors
Masaki Kameko
Department of Mathematics
Faculty of Regional Science
Toyama University of International Studies
65-1 Higashikuromaki
Toyama, 930-1292
Japan
Mamoru Mimura
Department of Mathematics
Faculty of Science
Okayama University
3-1-1 Tsushima-naka
Okayama, 700-8530
Japan