Computing equivariant stable homotopy classes of maps

Lukas Vokrinek
Thursday, July 25, 2013 - from 16:00 to 16:25
In a recent paper, \v{C}adek, Kr\v{c}\'{a}l, Matou\v{s}ek, Sergeraert, Vok\v{r}\'{i}nek and Wagner presented an algorithm for computing the abelian group of stable homotopy classes of maps between finite simplicial complexes. This algorithm is based on effective homological computations with Eilenberg--MacLane spaces whose origin lies in the work of Eilenberg and MacLane. I will report on a work in progress that extends our previous paper further to simplicial complexes equipped with free actions of a fixed finite group~$G$ and to equivariant stable homotopy classes of maps. This extension was motivated by the problem of deciding embeddability of simplicial complexes into Euclidean spaces.