Real Algebraic and Analytic Geometry |

Radial index and Poincaré-Hopf index of 1-forms on semi-analytic sets.

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Submission: 2009, March 12.

*Abstract:
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.

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