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The Equivariant Noncommutative AtiyahPatodiSinger Index Theorem ∗
, 2006
"... In [Wu], the noncommutative AtiyahPatodiSinger index theorem was proved. In this paper, we extend this theorem to the equivariant case. Keywords: Equivariant total eta invariants; Clifford asymptotics; C(1)Fredholm module; superconnection. ..."
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In [Wu], the noncommutative AtiyahPatodiSinger index theorem was proved. In this paper, we extend this theorem to the equivariant case. Keywords: Equivariant total eta invariants; Clifford asymptotics; C(1)Fredholm module; superconnection.
Equivariant etaInvariants and etaForms
, 1998
"... . Let a Lie group G act isometrically on an odd dimensional Riemannian manifold M and let D be a Gequivariant operator of Dirac type on M . We construct a formal power series j X (D) in X 2 g, which can be interpreted as a universal jform for families of Dirac operators induced by D over fibratio ..."
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fibrations with fibres isometric to M and with structure group G. For a Killing field X 2 g without zeroes, j rX (D) is the Taylor series of j e \GammarX (D)\Gamma f(rX). Here jg (D) for g 2 G is the Gequivariant jinvariant and f(X) is locally computable on M . Thus f describes the singularity of jg (D
THE ETA INVARIANT
"... \The eta invariant, equivariant bordism, connective K theory and manifolds with positive scalar curvature, " a dissertation prepared by Egidio BarreraYanez ..."
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\The eta invariant, equivariant bordism, connective K theory and manifolds with positive scalar curvature, " a dissertation prepared by Egidio BarreraYanez
Surgery and equivariant Yamabe invariant
, 2006
"... We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of Ginvariant metrics for a compact Lie group G. The GYamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit volume Ginvariant metrics minimizing the total scalar curvature ..."
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We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of Ginvariant metrics for a compact Lie group G. The GYamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit volume Ginvariant metrics minimizing the total scalar curvature
ETA INVARIANTS OF HOMOGENEOUS SPACES
, 2002
"... Abstract. We derive a formula for the ηinvariants of equivariant Dirac operators on quotients of compact Lie groups, and for their infinitesimally equivariant extension. As an example, we give some computations for spheres. Quotients M = G/H of compact Lie groups form a very special class of manifo ..."
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. First steps in this direction have been made in [G1]–[G3], however, one complicated (though local) term remained. The goal of this paper is to present a formula for the nonequivariant eta invariant η(D κ) that is more tractable. More generally, we also obtain a formula for the infinitesimally
THE ETA INVARIANT AND EQUIVARIANT BORDISM OF FLAT MANIFOLDS WITH CYCLIC HOLONOMY GROUP OF ODD PRIME ORDER
, 910
"... Abstract. We study the eta invariants of compact flat spin manifolds of dimension n with holonomy group Zp, where p is an odd prime. We find explicit expressions for the twisted and relative eta invariants and show that the reduced eta invariant is always an integer, except in a single case, when p ..."
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Abstract. We study the eta invariants of compact flat spin manifolds of dimension n with holonomy group Zp, where p is an odd prime. We find explicit expressions for the twisted and relative eta invariants and show that the reduced eta invariant is always an integer, except in a single case, when p
The equivariant Minkowski problem in Minkowski space
, 2014
"... The classical Minkowski problem in Minkowski space asks, for a positive function φ on Hd, for a convex set K in Minkowski space with C2 spacelike boundary S, such that φ(η)−1 is the Gauss–Kronecker curvature at the point with normal η. Analogously to the Euclidean case, it is possible to formulate ..."
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. The regular version was proved by T. Barbot, F. Béguin and A. Zeghib for d = 2 and by V. Oliker and U. Simon for Γτ = Γ. Our method is totally different. Moreover, we show that those cases are very specific: in general, there is no smooth Γτinvariant surface of constant GaussKronecker curvature equal to 1.
INDEX OF ΓEQUIVARIANT TOEPLITZ OPERATORS
, 1999
"... Abstract. Let Γ be a discrete subgroup of PSL(2, R) of infinite covolume with infinite conjugacy classes. Let Ht be the Hilbert space consisting of analytic functions in L2 (D, (Im z) t−2dzdz) and let, for t> 1, πt denote the corresponding projective unitary representation of PSL(2, R) on this Hi ..."
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) on this Hilbert space. We denote by At the II ∞ factor given by the commutant of πt(Γ) in B(Ht). Let F denote a fundamental domain for Γ in D and assume that t> 5. ∂M = ∂D ∩ F is given the topology of disjoint union of its connected components. Suppose that f is a continuous Γinvariant function on D whose
Documenta Math. 117 Equivariant Iwasawa Theory: An Example
, 2007
"... Abstract. The equivariant main conjecture of Iwasawa theory is shown to hold for a Galois extension K/k of totally real number fields with Galois group an ladic prol Lie group of dimension 1 containing an abelian subgroup of index l, provided that Iwasawa’s µinvariant µ(K/k) vanishes. ..."
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Abstract. The equivariant main conjecture of Iwasawa theory is shown to hold for a Galois extension K/k of totally real number fields with Galois group an ladic prol Lie group of dimension 1 containing an abelian subgroup of index l, provided that Iwasawa’s µinvariant µ(K/k) vanishes.
EQUIVARIANT ORBIFOLD STRUCTURES ON THE PROJECTIVE LINE AND INTEGRABLE HIERARCHIES
, 707
"... Abstract. Let CP 1 k,m be the orbifold structure on CP 1 obtained via uniformizing the neighborhoods of 0 and ∞ respectively by z ↦ → z k and w ↦ → w m. The diagonal action of the torus T = ( S 1) 2 on CP 1 induces naturally an action on the orbifold CP 1 k,m. In this paper we prove that if k and m ..."
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and m are coprime then Givental’s prediction of the equivariant total descendent GromovWitten potential of CP 1 k,m satisfies certain Hirota Quadratic Equations (HQE for short). We also show that after an appropriate change of the variables, similar to Getzler’s change in the equivariant Gromov
Results 1  10
of
43