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Equivariant map
About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.
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52 citations
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TL;DR: In this paper, a concrete numerical example of Z 6 -equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions.
Abstract: A concrete numerical example of Z 6 -equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H (2k + 1)≥(2 k + 1) 2 -1 for the perturbed Hamiltonian systems.
52 citations
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TL;DR: In this paper, the authors associate a class in the K-theory of the Grassmannian with equivariant localization and provide a geometric interpretation of the Tutte polynomial.
Abstract: To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial. We also extend results of the second author concerning the behavior of such classes under direct sum, series and parallel connection and two-sum; these results were previously only established for realizable matroids, and their earlier proofs were more difficult. R´ esum´ e. ` A chaque matronous associons une classe dans la K-thde la grassmannienne. Nous ´
52 citations
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TL;DR: For splice-quotient singularities, the authors showed that the equivariant, divisorial multi-variable Hilbert-Poincare series is topological and provided a combinatorial description of divisors of analytic function-germs.
52 citations
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TL;DR: In this paper, the p-part of the Equivariant Tamagawa Number Conjecture was proved for the pair (h 0 (Spec(L)), Z(Gal(L/K))).
Abstract: Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extension of k and let K be a subextension of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h 0 (Spec(L)), Z(Gal(L/K))).
52 citations