The Truncated Witten Genus
نویسنده
چکیده
In this paper we define and examine the truncated Witten genus. It is defined as the equivariant index of the Dirac operator on the manifold Map(Cp, M) with its natural Cp-action. Here, Map(Cp, M) is the space of maps from the cyclic group of order p into a closed, connected, spin manifold, By applying the Atiyah-Singer index theorem we give a topological formula for the truncated Witten genus which is related to the formula for the Witten genus by truncation of the infinite products. We also show that the equivariant index of the Dirac operator on the projective space PMap(Cp, C) is closely related to the truncated Witten genus of CP. The spaces PMap(Cp, C) define a filtration of the space PMap(S, C) which has been used to study equivariant objects on the smooth loop space of CP.
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