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Modular Forms and Topology (1996)
| Venue: | In Proc. of the AMS Conference on the Monster and Related Topics, Contemporary Math. |
| Citations: | 3 - 0 self |
BibTeX
@MISC{Liu96modularforms,
author = {Kefeng Liu},
title = {Modular Forms and Topology},
year = {1996}
}
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Abstract
We want to discuss various applications of modular forms in topology. The starting point is elliptic genus and its generalizations. The main techniques are the Atiyah-Singer index theorem, the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, Kac-Moody Lie algebras, modular forms and theta-functions. Just as the representations theory of classical Lie groups has close connections with the Atiyah-Singer index formula as exposed in [A1], the representation theory of loop groups plays very important role in our study. One of the most important new features of loop group representations is the modular invariance of the Kac-Weyl character formula, which allows us to derive many interesting new results and to unify many important old results in topology. In this paper we will develope along this line. We hope that the other features of loop group representations, such as fusion rules and tensor category structure may also be applied to topology. See the discussions in §3. The contents of this paper is organized in the following way. In §1 we introduce elliptic genus by combining index theory and the representation theory
Keyphrases
modular form representation theory loop group representation elliptic genus important role classical lie group atiyah-bott-segal-singer lefschetz kac-weyl character formula many important old result index theory tensor category structure new result modular invariance following way fusion rule atiyah-singer index formula atiyah-singer index theorem various application kac-moody lie algebra important new feature close connection point formula loop group main technique
