A homological approach to problems of compact group actions: Homologically bounded G-chain complexes

Speaker: William Browder. Lecure 2.

Abstract: We define homologicaly upper bounded, ('H*- upb') and show if C and C/G are both
H*-upb then the dimensions (top non zero cohomology dimension) are the same for
G a p-group (with F_p coefficients). In case C is 'coconnected ' (top homology Z) then
so is C/G and the quotient map has degree |G|. This gives an extension in this
context of my 1982 formula that |G| divides the product of the exponents of H^k+1(G; H_k(C)).
We define H*(G)- nilpotent and H*(G)- finite and show some elementary properties.