Equivariant map

About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.

Chern characters for proper equivariant homology theories and applications to K- and L-theory

Abstract: We construct for an equivariant homology theory for proper equiv- ariant CW-complexes an equivariant Chern character, provided that certain conditions are satisfied. This applies for instance to the sources of the assembly maps in the Farrell- Jones Conjecture with respect to the family F of finite subgroups and in the Baum- Connes Conjecture. Thus we get an explicit calculation in terms of group homology of Qn Z KnORGU and Qn Z LnORGU for a commutative ring R with QH R, provided the Farrell-Jones Conjecture with respect to F is true, and of QnZ K top n ˇ C r OG; FU for Fa R; C, provided the Baum-Connes Conjecture is true.

Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling

Abstract: We consider a ring of identical elements with time delayed, nearest-neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The bifurcation and stability of nontrivial asynchronous oscillations from the trivial solution are analysed using equivariant bifurcation theory and centre manifold construction.

Vertices, vortices & interacting surface operators

Abstract: We show that the vortex moduli space in non-abelian supersymmetric $ \mathcal{N} = \left( {{2},{2}} \right) $ gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations.

Equivariant chow cohomology of toric varieties

Abstract: We show that the equivariant Chow cohomology ring of a toric vari- ety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which lo- calization holds in equivariant Chow cohomology with integer coe!cients. We also compute the equivariant Chow cohomology of toric prevarieties and general complex hypertoric varieties in terms of piecewise polynomial functions. If X = X(!) is a smooth, complete complex toric variety then the follow- ing rings are canonically isomorphic: the equivariant singular cohomology ring H ! T (X), the equivariant Chow cohomology ring A ! (X), the Stanley-Riesner ring SR(!), and the ring of integral piecewise polynomial functions PP ! (!). If X is simplicial but not smooth then H ! (X) may have torsion and the natural map from SR(!) takes monomial generators to piecewise linear functions with ra- tional, but not necessarily integral, coe"cients. In such cases, these rings are not isomorphic, but they become isomorphic after tensoring with Q. When X is not simplicial, there are still natural maps between these rings, for instance from A ! (X)Q to H ! (X)Q and from H ! T (X) to PP ! (!), but these maps are far

Towards the Proof of AGT Relations with the Help of the Generalized Jack Polynomials

Abstract: Original proofs of the AGT relations with the help of the Hubbard–Stratanovich duality of the modified Dotsenko–Fateev matrix model did not work for β ≠ 1, because Nekrasov functions were not properly reproduced by Selberg–Kadell integrals of Jack polynomials. We demonstrate that if the generalized Jack polynomials, depending on the N-ples of Young diagrams from the very beginning, are used instead of the N-linear combinations of ordinary Jacks, this resolves the problem. Such polynomials naturally arise as special elements in the equivariant cohomologies of the GL(N)-instanton moduli spaces, and this also establishes connection to alternative ABBFLT approach to the AGT relations, studying the action of chiral algebras on the instanton moduli spaces. In this paper, we describe a complete proof of AGT in the simple case of GL(2) (N = 2) Yang–Mills theory, i.e., the 4-point spherical conformal block of the Virasoro algebra.