Torus equivariant elliptic cohomology and sigma orientations

Chen, Hsian-Yang

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https://hdl.handle.net/2142/16822 Copy

Description

Title

Torus equivariant elliptic cohomology and sigma orientations

Author(s)

Chen, Hsian-Yang

Issue Date

2010-08-20T17:58:52Z

Director of Research (if dissertation) or Advisor (if thesis)

Ando, Matthew

Doctoral Committee Chair(s)

Rezk, Charles

Committee Member(s)

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

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• elliptic cohomology
• sigma orientation

Abstract

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.

Graduation Semester

2010-08

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

Copyright and License Information

Copyright 2010 Hsian-Yang Chen

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