arXiv subjects
Publications and source records attributed to Quitzeh Morales Meléndez.
There are different notions of homology and cohomology that can be defined for a group with an action of another group by group automorphisms. In this paper we address three natural questions that arise in this context. Namely, the relation of these notions with the usual (co)homology of a semidirect product, the interpretation of the first homology group as some kind of abelianization and the classification of (invariant) group extensions.
In the paper "Aquino, C., Jiménez, R., Mijangos, M., Morales Meléndez, Q.: On Invariant (co)homology of a group, preprint" are introduced two groups generated by the orbits of an action of a group on another group by automorphisms. One is of group-theoretic nature and the other comes from homology of invariant group chains. In this note are given some properties of the first groups and is studied a natural homomorphism between these groups. More precisely, it is shown that this homomorphism is not injective nor surjective. A description of the kernel is given. Note: there was a previous version with an error in the construction. The error has been corrected now.
In this short note we compare Mishchenko's definition of noncommutative signature for a manifold with proper $G$-action of a discrete, countable group $G$ with the (more analytical) counterpart defined by Higson and Roe in the series of articles "Mapping Surgery to Analysis". A generalization of the coarse index is also addressed.
In this paper are defined cohomology-like groups that classify loop extensions satisfying a given identity in three variables for association identities, and in two variables for the case of commutativity. It is considered a large amount of identities. This groups generalize those defined in works of Nishigori [2] and of Jhonson and Leedham-Green [4]. It is computed the number of metacyclic extensions for trivial action of the quotient on the kernel in one particular case for left Bol loops and in general for commutative loops.
In this work the equivariant signature of a manifold with proper action of a discrete group is defined as an invariant of equivariant bordisms. It is shown that the computation of this signature can be reduced to its computation on fixed points sets equipped with their tubular neighborhoods. It is given a description of the equivariant vector bundles with action of a discrete group $G$ for the case when the action over the base is proper quasi-free, i.e. the stationary subgroup of any point is finite. The description is given in terms of some classifying space.
In this article we generalize the results of the previous article with the same title [arXiv:0901.3308] for the case of an arbitrariy linear representation and non-normal stationary subgroup.
We give a description of the vector $G$-bundles over $G$-spaces with quasi-free proper action of discrete group $G$ in terms of the classifying space.