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41.
For a finite group G we define an involution on the equivariant Whitehead group given by reversing the direction of an equivariant h-cobordism. It turns out that the involution is not compatible with the splitting of the equivariant Whitehead group into a direct sum of algebraic Whitehead groups, certain correction terms involving the transfer maps of the normal sphere bundles of the various fixed point sets come in. However, if the group has odd order, these transfer maps all vanish. We prove a duality formula for a G-homotopy equivalence (f f): (M; M) (N, N) relating the equivariant Whitehead torsion of f and (f,f). 相似文献
42.
In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed's odd dimensional index formula. Then we extend this theorem to the noncommutative geometry framework. As a corollary, we get the odd family Lichnerowicz vanishing theorem and the odd family Atiyah-Hirzebruch vanishing theorem. 相似文献
43.
44.
In this paper, a statistical prediction problem under ordered location and scale parameters are considered. Double-shrinkage predictors are given which use all the available data and improve on single-shrinkage predictors, and hence the best equivariant predictors. 相似文献
45.
Jocelino Sato Vicente Francisco De Souza Neto 《Annals of Global Analysis and Geometry》2006,29(3):221-240
We classify the zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in the euclidean space ℝ
p+q+2, p,q > 1, analyzing whether they are embedded and stable. The Morse index of the complete hypersurfaces show the existence of embedded, complete and globally stable zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in ℝ
p+q+2, p+q≥ 7, which are not homeomorphic to ℝ
p+q+1. Such stable examples provide counter-examples to a Bernstein-type conjecture in the stable class, for immersions with zero scalar curvature.
Mathematics Subject Classifications (2000): 53A10, 53C42,49005. 相似文献
46.
David S. Metzler 《Transactions of the American Mathematical Society》2000,352(8):3495-3521
We use symplectic cobordism, and the localization result of Ginzburg, Guillemin, and Karshon to find a wall-crossing formula for the signature of regular symplectic quotients of Hamiltonian torus actions. The formula is recursive, depending ultimately on fixed point data. In the case of a circle action, we obtain a formula for the signature of singular quotients as well. We also show how formulas for the Poincaré polynomial and the Euler characteristic (equivalent to those of Kirwan can be expressed in the same recursive manner.
47.
Debashish Goswami 《Proceedings Mathematical Sciences》2009,119(1):63-70
We prove that an arbitrary (not necessarily countably generated) Hilbert G - module on a G - C
* algebra admits an equivariant embedding into a trivial G - module, provided G is a compact Lie group and its action on is ergodic. 相似文献
48.
Adam Korá nyi Ró bert Szoke 《Proceedings of the American Mathematical Society》2006,134(12):3449-3456
We prove an equivariant analogue of Chevalley's isomorphism theorem for polynomial, or maps.
49.
Shangjiang Guo Jeroen S. W. Lamb 《Proceedings of the American Mathematical Society》2008,136(6):2031-2041
In this paper we employ an equivariant Lyapunov-Schmidt procedure to give a clearer understanding of the one-to-one correspondence of the periodic solutions of a system of neutral functional differential equations with the zeros of the reduced bifurcation map, and then set up equivariant Hopf bifurcation theory. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions in terms of the original system, avoiding the process of center manifold reduction.
50.
Hon-kit Wai 《Transactions of the American Mathematical Society》1999,351(6):2141-2182
Given an -invariant Morse function and an -invariant Riemannian metric , a family of finite dimensional subcomplexes , , of the Witten deformation of the -equivariant de Rham complex is constructed, by studying the asymptotic behavior of the spectrum of the corresponding Laplacian as . In fact the spectrum of can be separated into the small eigenvalues, finite eigenvalues and the large eigenvalues. Then one obtains as the complex of eigenforms corresponding to the small eigenvalues of . This permits us to verify the -equivariant Morse inequalities. Moreover suppose is self-indexing and satisfies the Morse-Smale condition, then it is shown that this family of subcomplexes converges as to a geometric complex which is induced by and calculates the -equivariant cohomology of .