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2009 Secondary characteristic classes of surface bundles
Søren Galatius
Algebr. Geom. Topol. 9(1): 293-303 (2009). DOI: 10.2140/agt.2009.9.293

Abstract

The Miller–Morita–Mumford classes associate to an oriented surface bundle EB 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 (p1). In this note we prove that the p2 reduction κi(E)H2i(B;p2) vanishes when i+1 is divisible by p(p1). We also define for each integer i1 a characteristic class λi(E)H2i(p1)2(B;p) which satisfies pλi(E)=κi(p1)1(E)H(B;p2).

Citation

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Søren Galatius. "Secondary characteristic classes of surface bundles." Algebr. Geom. Topol. 9 (1) 293 - 303, 2009. https://doi.org/10.2140/agt.2009.9.293

Information

Received: 27 February 2008; Revised: 26 September 2008; Accepted: 29 September 2008; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1166.55004
MathSciNet: MR2482078
Digital Object Identifier: 10.2140/agt.2009.9.293

Subjects:
Primary: 55R40

Rights: Copyright © 2009 Mathematical Sciences Publishers

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