We show that certain canonical realizations of the complexes Hom(G,H) and Hom+(G,H) of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For G a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of ...

In this work, the notion of a twisted partial Hom-Hopf action is introduced, and conditions on cocycles are established in order to construct Hom-crossed products. Also, equivalence products discussed. Finally, we shall describe coquasitriangular structures

We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we construct certain q-deformations of the usual sl(2)-action on the affine plane.

In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain to the other to be itself represented by a vector bundle. We apply this to present a more transparent version of an earlier construction of limit linear serie...

We define generalizations of the Albanese variety for a projective variety X. The generalized Albanese morphisms X albr // _ _ _ Albr(X) contract those curves C in X for which the induced morphism Hom(π1(X),U(r)) → Hom(π1(C),U(r)) has a finite image. Thus, they may be interpreted as a U(r)-version of the Shafarevich morphism.

In this paper, we introduced the concept of crossed modules for Hom–Lie antialgebras. It is proved that category antialgebras and [Formula: see text]-Hom–Lie are equivalent to each other. The relationship between extension third cohomology group investigated.

J. P. MAY I will give a philosophical overview of some joint work with Igor Kriz (in algebra), with Tony Elmendorf and Kriz (in topology), and with John Greenlees (in equivariant topology). I will begin with a description of some foundational issues before saying anything about the applications. This is not the best way to motivate people, but I must explain the issues involved in order to desc...