郇真 博士:Quasi-elliptic cohomology

讲座时间 Datetime: 
星期五, 2018/01/12 - 16:0017:30
地点 Venue: 
海滨红楼6号楼1楼会议室
报告人 Speaker: 
郇真 博士
单位 Affiliation: 
中山大学数学学院
报告摘要 Abstract: 

Quasi-elliptic cohomology is closely related to Tate K-theory, which is the generalized elliptic cohomology associate to Tate curve. Quasi-elliptic cohomology 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 proved the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. Moreover, we construct a G-orthogonal spectra weakly representing quasi-elliptic cohomology. Unfortunately, our construction does not arise from a global spectra; thus,  we consider a new formulation of global stable homotopy theory that contains quasi-elliptic cohomology.