Torus equivariant elliptic cohomology and sigma orientations

Let $ \mathcal{C} \colon= \mathds{C}/ \Lambda$ be a complex elliptic curve. In this paper, we give a detailed construction of torus equivariant elliptic cohomology, which is a sheaf of \mathcal{ O}_{\mathcal{C}ⁿ}-algebras over \mathcal{C}ⁿ. As applications, we construct global sections for sigma functions and relates these sections to the elliptic orbifold genera.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Chen, Hsian-Yang

Contributors dc:contributor

• Ando, Matthew
• Rezk, Charles
• McCarthy, Randy
• Guillou, Bertrand

• elliptic cohomology
• sigma orientation

Statement dc:rights

• Copyright 2010 Hsian-Yang Chen

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16822

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16822