The Signature of a Manifold
Rodriguez, Jose
arXiv, 0508181 / Harvested from arXiv
Text on arXiv
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 2k-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. This second version includes corrections and many examples.
Publié le : 2005-08-10
Classification:  Mathematics - Differential Geometry,  Mathematical Physics,  5301, 5701 
@article{0508181,
     author = {Rodriguez, Jose},
     title = {The Signature of a Manifold},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508181}
}

Rodriguez, Jose. The Signature of a Manifold. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508181/