The purpose of this note is to prove the converse of the Lefschetz fixed point theorem (CLT) together with an equivariant version of the converse of the Lefschetz deformation theorem (CDT) in the category of finite G-simplicial complexes, where G is a finite group.
Let p be a prime number and X a simply connected Hausdorff space equipped with a free -action generated by . Let be a homeomorphism generating a free -action on the (2n-1)-sphere, whose orbit space is some lens space. We prove that, under some homotopy conditions on X, there exists an equivariant map . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.
If is a -dim polyhedran, then using geometric techniques, we construct groups and such that there are natural isomorphisms and which induce an intersection pairing. These groups give a geometric interpretation of two spectral sequences studied by Zeeman and allow us to prove a conjecture of Zeeman about them.
We prove a Z-set unknotting theorem for Nöbeling spaces.