Geodesic
Cohomology of preimages with local coefficients
Gonçalves, Daciberg Lima1 ; Wong, Peter2
1Dept. de Matemática, IME - USP, Caixa Postal 66.281, CEP 05311-970 São Paulo - SP, Brasil
2Department of Mathematics, Bates College, Lewiston, ME 04240, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1471-1489
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Let M,N and B ⊂ N be compact smooth manifolds of dimensions n + k,n and ℓ, respectively. Given a map f : M → N, we give homological conditions under which g−1(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,N−B) is Poincaré dual (with local coefficients) under f∗ to the image of a corresponding class in Hn+k−j(f−1(B)) when f is transverse to B. This generalizes a similar formula of D Gottlieb in the case of simple coefficients.

DOI : 10.2140/agt.2006.6.1471
Keywords: fibration, local trivial fibration, Poincaré duality, local coefficient system, (co)homology with local coefficients

Gonçalves, Daciberg Lima  1   ; Wong, Peter  2

1 Dept. de Matemática, IME - USP, Caixa Postal 66.281, CEP 05311-970 São Paulo - SP, Brasil
2 Department of Mathematics, Bates College, Lewiston, ME 04240, USA 
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Gonçalves, Daciberg Lima; Wong, Peter. Cohomology of preimages with local coefficients. Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1471-1489. doi: 10.2140/agt.2006.6.1471

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