Elliptic Quasicomplexes on Compact Closed Manifolds

Details Elliptic Quasicomplexes on Compact Closed Manifolds Elliptic Quasicomplexes on Compact Closed Manifolds

2011-09-16

arxiv.org/abs/1109.3557v1

Mathematics

Analysis of PDEs

Scientific paper

We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the zero section. We prove that elliptic quasicomplexes are Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes and prove a generalization of the Atiyah-Singer index theorem.

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