Cohomology of preimages with local coefficients
نویسندگان
چکیده
Let M,N and B ⊂ N be compact smooth manifolds of dimensions n + k, n and ` , 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(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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