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On the Stiefel–Whitney classes of the representations associated with Spin(15)

Mamoru Mimura and Tetsu Nishimoto

Geometry & Topology Monographs 11 (2007) 141–176

DOI: 10.2140/gtm.2007.11.141

arXiv: 0903.4969

Abstract

We determine the Stiefel–Whitney classes of the second exterior representation and the spin representation of Spin(15), which are useful to calculate the mod 2 cohomology of the classifying space of the exceptional Lie group E8.

Keywords

Stiefel–Whitney class, classifying space, spinor group, exceptional Lie group, representation

Mathematical Subject Classification

Primary: 55R40

Secondary: 22E46

References
Publication

Received: 25 February 2005
Accepted: 17 June 2005
Published: 14 November 2007

Authors
Mamoru Mimura
Department of Mathematics
Faculty of Science
Okayama University
3-1 Tsushima-naka, Okayama 700-8530
Japan
Tetsu Nishimoto
Department of Welfare Business
Kinki Welfare University
Fukusaki-cho, Hyogo 679-2217
Japan