Algebra/Topology Seminar

Speaker: Zhen Huan (Huazhong University of Science and Technology)

Title: Quasi-elliptic cohomology and related problems
Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic cohomology theories.  It can be interpreted by orbifold loop spaces and expressed in terms of equivariant K-theories. We formulate the complete power operation of this theory. Applying that we prove the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. In addition, twisted quasi-elliptic cohomology can be defined. We construct a twisted Chern character map from it to the twisted equivariant elliptic cohomology. Moreover, we construct a G-orthogonal spectra weakly representing quasi-elliptic cohomology.  
We are still studying some problems of elliptic cohomology via quasi-elliptic cohomology, for example, whether we can find any relation between quasi-elliptic cohomology of a 2-group and Lurie’s 2-equivariant elliptic cohomology theory.