The homology of a homotopy inverse limit can be studied by a spectral sequence with has E2 term the derived functors of limit in the category of coalgebras. These derived functors can be computed using the theory of Dieudonné modules if one has a diagram of connected abelian Hopf algebras. One of the standard problems in homotopy theory is to calculate the homology of a given type of inverse li...

Up to oriented homotopy equivalence, a PD–pair (X, ∂X) with aspherical boundary components is uniquely determined by the Π1–system {κi : Π1(∂Xi, ∗) → Π1(X, ∗)}i∈J , the orientation character ωX ∈ H(X;Z/2Z) and the image of the fundamental class [X, ∂X] ∈ H3(X, ∂X;Z) under the classifying map [3]. We call the triple ({κi}i∈J , ωX , [X, ∂X]) the fundamental triple of the PD–pair (X, ∂X). Using Pe...

In this talk, I will introduce and motivate the main objects of study in modular representation theory, which leads one to consider the stable module category. Perhaps surprisingly, one can do homotopy theory in this setting, as the stable module category has the structure of a stable model category. Therefore, there is a very rich interplay between modular representation theory and stable homo...

Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...