Radial Index and Poincaré-hopf Index of 1-forms on Semi-analytic Sets
نویسندگان
چکیده
The radial index of a 1-form on a singular set is a generalization of the classical Poincaré-Hopf index. We consider different classes of closed singular semi-analytic sets in R that contain 0 in their singular locus and we relate the radial index of a 1-form at 0 on these sets to Poincaré-Hopf indices at 0 of vector fields defined on R.
منابع مشابه
A theorem of Poincaré-Hopf type
We compute (algebraically) the Euler characteristic of a complex of sheaves with constructible cohomology. A stratified Poincaré-Hopf formula is then a consequence of the smooth Poincaré-Hopf theorem and of additivity of the Euler-Poincaré characteristic with compact supports, once we have a suitable definition of index. AMS classification: 55N33 57R25
متن کاملA Poincaré-Hopf type formula for Chern character numbers
For two complex vector bundles admitting a homomorphism with isolated singularities between them, we establish a Poincaré-Hopf type formula for the difference of the Chern character numbers of these two vector bundles. As a consequence, we extend the original Poincaré-Hopf index formula to the case of complex vector fields.
متن کاملConvex Generalized Semi-Infinite Programming Problems with Constraint Sets: Necessary Conditions
We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...
متن کاملAbout the Euler-poincaré Characteristic of Semi-algebraic Sets Defined with Two Inequalities
We express the Euler-Poincaré characteristic of a semi-algebraic set, which is the intersection of a non-singular complete intersection with two polynomial inequalities, in terms of the signatures of appropriate bilinear symmetric forms.
متن کاملTopological Semimetals carrying Arbitrary Hopf Numbers: Hopf-Link, Solomon’s-Knot, Trefoil-Knot and Other Semimetals
We propose a new type of Hopf semimetals indexed by a pair of numbers (p, q), where the Hopf number is given by pq. The Fermi surface is given by the preimage of the Hopf map, which consists of loops nontrivially linked for a nonzero Hopf number. The Fermi surface forms a torus link, whose examples are the Hopf link indexed by (1, 1), the Solomon’s knot (2, 1), the double Hopf-link (2, 2) and t...
متن کامل