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Torus equivariant elliptic cohomology and sigma orientations

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Title: Torus equivariant elliptic cohomology and sigma orientations
Author(s): Chen, Hsian-Yang
Director of Research: Ando, Matthew
Doctoral Committee Chair(s): Rezk, Charles
Doctoral Committee Member(s): Ando, Matthew; McCarthy, Randy; Guillou, Bertrand
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(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.
Issue Date: 2010-08-20
URI: http://hdl.handle.net/2142/16822
Rights Information: Copyright 2010 Hsian-Yang Chen
Date Available in IDEALS: 2010-08-20
Date Deposited: 2010-08
 

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