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2006 Cohomology of preimages with local coefficients
Daciberg Lima Gonçalves, Peter Wong
Algebr. Geom. Topol. 6(3): 1471-1489 (2006). DOI: 10.2140/agt.2006.6.1471

Abstract

Let M,N and BN be compact smooth manifolds of dimensions n+k,n and , respectively. Given a map f:MN, we give homological conditions under which g1(B) has nontrivial cohomology (with local coefficients) for any map g homotopic to f. We also show that a certain cohomology class in Hj(N,NB) is Poincaré dual (with local coefficients) under f to the image of a corresponding class in Hn+kj(f1(B)) when f is transverse to B. This generalizes a similar formula of D Gottlieb in the case of simple coefficients.

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Daciberg Lima Gonçalves. Peter Wong. "Cohomology of preimages with local coefficients." Algebr. Geom. Topol. 6 (3) 1471 - 1489, 2006. https://doi.org/10.2140/agt.2006.6.1471

Information

Received: 16 March 2005; Revised: 25 April 2006; Accepted: 14 August 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1129.55001
MathSciNet: MR2253456
Digital Object Identifier: 10.2140/agt.2006.6.1471

Subjects:
Primary: ‎55M20
Secondary: 55S35

Rights: Copyright © 2006 Mathematical Sciences Publishers

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