Volume 9, issue 1 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Secondary characteristic classes of surface bundles

Søren Galatius

Algebraic & Geometric Topology 9 (2009) 293–303
Abstract

The Miller–Morita–Mumford classes associate to an oriented surface bundle E B a class κi(E) H2i(B; ). It was proved by the author, Madsen and Tillman [J. Amer. Math. Soc. 19 (2006) 759-779] that the mod p reduction κi(E) H2i(B; p) vanishes when i + 1 is divisible by (p 1). In this note we prove that the p2 reduction κi(E) H2i(B; p2) vanishes when i + 1 is divisible by p(p 1). We also define for each integer i 1 a characteristic class λi(E) H2i(p1)2(B; p) which satisfies pλi(E) = κi(p1)1(E) H(B; p2).

Keywords
mapping class group, characteristic class, Toda bracket
Mathematical Subject Classification 2000
Primary: 55R40
References
Publication
Received: 27 February 2008
Revised: 26 September 2008
Accepted: 29 September 2008
Published: 19 February 2009
Authors
Søren Galatius
Department of Mathematics
Stanford University
Stanford, CA 94305
USA