Browsing by Subject "Cobordism"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Open Access Cobordism calculations with Adams and James spectral sequences(2010) Erdal, Mehmet AkifLet ξn : Z/p → U(n) be an n-dimensional faithful complex representation of Z/p and in : U(n)→O(2n) be inclusion for n ≥ 1. Then the compositions in ◦ ξn and jn ◦ in ◦ ξn induce fibrations on BZ/p where jn : O(2n) → O(2n + 1) is the usual inclusion. Let (BZ/p, f) be a sequence of fibrations where f2n : BZ/p→BO(2n) is the composition Bin ◦ Bξn and f2n+1 : BZ/p→BO(2n + 1) is the composition Bjn ◦Bin ◦Bξn. By Pontrjagin-Thom theorem the cobordism group Ωm(BZ/p, f) of m-dimensional (BZ/p, f) manifolds is isomorphic to π s m(MZ/p, ∗) where MZ/p denotes the Thom space of the bundle over BZ/p that pullbacks to the normal bundle of manifolds representing elements in Ωm(BZ/p, f). We will use the Adams and James Spectral Sequences to get information about Ωm(BZ/p, f), when p = 3.Item Open Access On smooth manifolds with the homotopy type of a homology sphere(Elsevier, 2018) Erdal, Mehmet AkifIn this paper we study M(X), the set of diffeomorphism classes of smooth manifolds with the simple homotopy type of X, via a map Ψ from M(X) into the quotient of K(X)=[X,BSO] by the action of the group of homotopy classes of simple self equivalences of X. The map Ψ describes which bundles over X can occur as normal bundles of manifolds in M(X). We determine the image of Ψ when X belongs to a certain class of homology spheres. In particular, we find conditions on elements of K(X) that guarantee they are pullbacks of normal bundles of manifolds in M(X).