Real Algebraic and Analytic Geometry

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275. Nicolas Dutertre:
Radial index and Poincaré-Hopf index of 1-forms on semi-analytic sets.


Submission: 2009, March 12.

The radial index of a $1$-form on a singular set is a generalization of the classical Poincar\'e-Hopf index. We consider different classes of closed singular semi-analytic sets in $\mathbb{R}^n$ that contain $0$ in their singular locus and we relate the radial index of a $1$-form at $0$ on these sets to Poincar\'e-Hopf indices at $0$ of vector fields defined on $\mathbb{R}^n$.

Mathematics Subject Classification (2000): 14B05, 14P15, 58K45.

Full text, 38p.: dvi 195k, ps.gz 255k, pdf 322k.

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