EQUIVARIANT DIFFERENTIAL TOPOLOGYt
نویسنده
چکیده
Section 2 concerns the classification of G-vector bundles. The precise statement is: The equivalence classes of k-dimensional G-vector bundles over M” “ subordinate ” to Pare in a natural one-to-one correspondence with the equivariant homotopy classes of maps of M into Gk( V’), the grassmannian of k-planes in V’, if t > n + k. The existence of a classifying map is proved via a transversality argument. The equivalence of bundles induced by homotopic maps can be shown to follow from the existence and uniqueness of solution curves of vector fields. Atiyah [l] has proved a similar theorem for compact topological spaces.
منابع مشابه
Equivariant heat invariants of the Laplacian and nonmininmal operators on differential forms
In this paper, we compute the first two equivariant heat kernel coefficients of the Bochner Laplacian on differential forms. The first two equivariant heat kernel coefficients of the Bochner Laplacian with torsion are also given. We also study the equivariant heat kernel coefficients of nonmininmal operators on differential forms and get the equivariant Gilkey-Branson-Fulling formula. MSC: 58J0...
متن کاملdG, δ-LEMMA FOR EQUIVARIANT DIFFERENTIAL FORMS WITH GENERALIZED COEFFICIENT
Consider a Hamiltonian action of a compact Lie Group on a symplectic manifold which has the strong Lefschetz property. We establish an equivariant version of the Merkulov-Guillemin dδ-lemma for equivariant differential forms with smooth or distributional coefficient. As a corollary we also obtain a version of equivariant formality theorem in this case.
متن کاملEquivariant Hopf Bifurcation in a Ring of Identical Cells with Delay
A kind of delay neural network with n elements is considered. By analyzing the distribution of the eigenvalues, a bifurcation set is given in an appropriate parameter space. Then by using the theory of equivariant Hopf bifurcations of ordinary differential equations due to Golubitsky et al. 1988 and delay differential equations due to Wu 1998 , and combining the normal form theory of functional...
متن کاملRing structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کاملNotes on Mirror Symmetry
1 Equivariant Cohomology 1 1.1 Group cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Equivariant cohomology of topological spaces . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Equivariant vector bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Equivariant pushforward . . . . . . . . . . . . . . . . . . . . . . . ....
متن کامل