Homological algebra for minimal Euler characteristics for certain manifolds

For given group G one of the open problems in algebraic topology is determining the minimal Euler characteristics of a manifold M which has the fundamental group G. If M is 2n-dimensional manifold and has (n − 1)-connected universal cover, Adem and Hambleton define the invariant q_2n(G) for the minimal Euler characteristic and they give an upper and lower bound for this invariant. In this thesis, our aim is to expound this estimation of Adem and Hambleton in [2, Theorem A]. In particular, we have studied the underlying homological algebraic tools, such as Ext, Tor and Heller shift in the stable category, which are necessary for this estimation.

Subject Keywords

Euler characteristic, homological algebra, Heller shift, stable category