Elliptic Genera and Vertex Operator Super-Algebras

Hirotaka Tamanoi (auth.)3540660062, 9783540660064

This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.

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Table of contents :
Introduction and summary of results….Pages 1-21
Elliptic genera….Pages 22-48
Vertex operator super algebras….Pages 49-92
G -invariant vertex operator super subalgebras….Pages 93-221
Geometric structure in vector spaces and reduction of structure groups on manifolds….Pages 222-302
Infinite dimensional symmetries in elliptic genera for Kähler manifolds….Pages 303-378