an:00912192
Zbl 0858.57034
Liu, Kefeng
On elliptic genera and theta-functions
EN
Topology 35, No. 3, 617-640 (1996).
00032759
1996
j
57R20 58J20 58J26
Witten rigidity theorem; elliptic operators; loop spaces; loop groups; elliptic genera; theta functions
The author gives a unified new proof of the Witten rigidity theorem for some elliptic operators commuting with a circle action. He makes essential use of a new feature of loop spaces and loop groups, the modular invariance. Actually he shows that modular invariance implies rigidity. Some new properties of elliptic genera and their relationships with theta functions are also discussed.
F.Gomez (Malaga)