An explicit formula for the transversal indices of the lifted Dolbeault operators
Differential Geometry
2016-12-30 v1 Spectral Theory
Abstract
M. F. Atiyah proved that the index of a transversally elliptic operator relative to a free action can be computed by using indices of elliptic operators on the orbit manifold. In this paper, we derive an explicit formula for the transversal indices on S^1-bundles over complex projective spaces. Using this explicit formula and the index map, we prove Lefschetz formula for the n-dimensional complex projective space with the canonical action of T^{n + 1}.
Keywords
Cite
@article{arxiv.1612.08887,
title = {An explicit formula for the transversal indices of the lifted Dolbeault operators},
author = {Naoto Miseki},
journal= {arXiv preprint arXiv:1612.08887},
year = {2016}
}
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34 pages