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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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