Quasi-Elliptic Cohomology I

Abstract

Quasi-elliptic cohomology is a variant of elliptic cohomology theories. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. Thus, the constructions on it can be made in a neat way. This theory reflects the geometric nature of the Tate curve. In this paper we provide a systematic introduction of its construction and definition.

Final Version. 26 pages. To appear in Advances in Mathematics. In this paper we generalize the construction in arXiv:1612.00930. The subtle point of this generalization is explained in Section 2