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Nilpotency and triviality of mod p Morita-Mumford classes of mapping class groups of surfaces

Published online by Cambridge University Press:  22 January 2016

Toshiyuki Akita
Toshiyuki Akita*
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan, akita@math.sci.hokudai.ac.jp
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Abstract

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This paper is concerned with mod p Morita-Mumford classes of the mapping class group Γg of a closed oriented surface of genus g ≥ 2, especially triviality and nontriviality of them. It is proved that is nilpotent if n ≡ − 1 (mod p − 1), while the stable mod p Morita-Mumford class is proved to be nontrivial and not nilpotent if n ≢ −1 (mod p − 1). With these results in mind, we conjecture that vanishes whenever n ≡ − 1 (mod p − 1), and obtain a few pieces of supporting evidence.

Keywords

55R4057R2014H3720J06
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 165 , March 2002 , pp. 1 - 22
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

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