turkmath.org

Let G be a finite p-group and k be a field of characteristic p. A topological space X is called an n-Moore space if its reduced homology is nonzero only in dimension n. We call a G-CW-complex X a Moore G-space over k if for every subgroup H of G, the fixed point set X^H is a Moore space with coefficients in k. A kG-module M is called an endo-permutation module if End_k (M) is a permutation kG-module. We show that if X is a finite Moore G-space, then the reduced homology module of X is an endo-permutation kG-module generated by relative syzygies. We consider the Grothendieck group of finite Moore G-spaces with addition given by the join operation, and relate this group to the Dade group generated by relative syzygies. In the talk I will give the necessary background on Moore G-spaces and Dade group, and provide many examples to motivate the statements of the theorems.