Geodesic
On the vanishing of characteristic numbers
Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 185-204.

Voir la notice de l'article provenant de la source International Press of Boston

In this article we introduce the notion of pure type for Killing vector fields on compact Riemannian and almost-Hermitian manifolds and present an application of the celebrated Atiyah-Bott-Singer localization formula for these Killing vector fields. Our central result is that if a $4n$-dimensional compact Riemannian manifold has a Killing vector field of pure type such that the dimension of its zero point set is less than $n$, then the vanishing statements for low-degree polynomials as given by the Atiyah-Bott-Singer localization formula imply the vanishing of Pontrjagin numbers of this manifold. An analogous result for the Chern numbers of compact almost-Hermitian manifolds is also established. The main strategy of our proof is to construct a family of lower-degree polynomials originating from the monomial symmetric polynomials.
DOI : 10.4310/HHA.2014.v16.n2.a10
Classification : 57R20, 57R25, 58J20
Keywords: Atiyah-Bott-Singer localization formula, characteristic number, semi-free circle action, monomial symmetric polynomial 
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     author = {Ping Li},
     title = {On the vanishing of characteristic numbers},
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     pages = {185--204},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a10/}
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Ping Li. On the vanishing of characteristic numbers. Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 185-204. doi : 10.4310/HHA.2014.v16.n2.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a10/

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