A new short proof of the local index formula and some of its applications

Details A new short proof of the local index formula and some of its applications A new short proof of the local index formula and some of its applications

2002-11-20

arxiv.org/abs/math/0211333v5

Comm. Math. Phys. 241 (2003) 215-234

Mathematics

Differential Geometry

v5: more typos fixed; 19 pages

Scientific paper

10.1007/s00220-003-0915-4

We give a new short proof of the index formula of Atiyah and Singer based on combining Getzler's rescaling with Greiner's approach of the heat kernel asymptotics. As application we can easily compute the Connes-Moscovici cyclic cocycle of even and odd Dirac spectral triples, and then recover the Atiyah-Singer index formula (even case) and the Atiyah-Patodi-Singer spectral flow formula (odd case).

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