The Signature of a Manifold

Details The Signature of a Manifold The Signature of a Manifold

2005-08-10

arxiv.org/abs/math/0508181v1

Mathematics

Differential Geometry

16 pages

Scientific paper

Let us consider a compact oriented riemannian manifold M without boundary and of dimension n=4k. The signature of M is defined as the signature of a given quadratic form Q. Two different products could be used to define Q and they render equivalent definitions: the exterior product of forms and the cup product of cohomology classes. The signature of a manifold is proved to yield a topological invariant. Additionally, using the metric, a suitable Dirac operator can be defined whose index coincides with the signature of the manifold.

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