Equivariant de Rham torsions

• 成果类型: Article
• 署名作者: Bismut, JM; Goette, S
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.159.53
• 发表日期: 2004
• 页码: 53-216
• 关键词: real analytic-torsion; singer index theorem; bott-chern currents; heat-equation; Riemannian manifolds; dynamical systems; vector-bundles; r-torsion; forms; superconnections

摘要

The purpose of this paper is to give an explicit local formula for the difference of two natural versions of equivariant analytic torsion in de Rham theory. This difference is the sum of the integral of a Chern-Simons current and of a new invariant, the V-invariant of an odd dimensional manifold equipped with an action of a compact Lie group. The V-invariant localizes on the critical manifolds of invariant Morse-Bott functions. The results in this paper are shown to be compatible with results of Bunke, and also our with previous results on analytic torsion forms.