A Lefschetz fixed point formula for symplectomorphisms

Details A Lefschetz fixed point formula for symplectomorphisms A Lefschetz fixed point formula for symplectomorphisms

2010-05-19

arxiv.org/abs/1005.3443v1

Mathematics

Symplectic Geometry

23 pages

Scientific paper

Consider a compact K\"ahler manifold endowed with a prequantum bundle. Following the geometric quantization scheme, the associated quantum spaces are the spaces of holomorphic sections of the tensor powers of the prequantum bundle. In this paper we construct an asymptotic representation of the prequantum bundle automorphism group in these quantum spaces. We estimate the characters of these representations under some transversality assumption. The formula obtained generalizes in some sense the Lefschetz fixed point formula for the automorphisms of the prequantum bundle preserving its holomorphic structure. Our results will be applied in two forthcoming papers to the quantum representation of the mapping class group.

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