A Gauss-Bonnet theorem, Chern classes and an adjunction formula for reductive groups
By: by Valentina Kiritchenko.
Published: 2004
Language: eng
Number of pages: 53
Description: My thesis is about geometry of reductive groups. The purpose is to extend some well-known geometric results that hold for the complex torus   &parl0;C*&parr0;n   to the case of an arbitrary complex reductive group. The thesis consists of two parts.The first part contains an analog of the Gauss-Bonnet theorem for constructible sheaves equivariant under the adjoint action. This theorem relates the Euler characteristic of a sheaf to the Gaussian degrees of the components of its characteristic cycle. As a corollary I get that a perverse sheaf equivariant under the adjoint action has nonnegative Euler characteristic.The common feature of the results and constructions of my thesis is that I use a group action to extend to noncompact setting such classical results as the Gauss-Bonnet theorem and the adjunction formula.In the second part, I modify one of the classical definitions of the Chern classes to construct noncompact analogs of the Chern classes for equivariant vector bundles over reductive groups. These Chern classes have the same properties as the usual Chern classes. Using the Chern classes of the tangent bundle, I obtain an adjunction formula for the Euler characteristic of hypersurfaces in arbitrary reductive groups.
Notes: Advisers:  A. Khovanskii; M. Kapzanov.

Thesis (Ph.D.)--University of Toronto, 2004.

Electronic version licensed for access by U. of T. users.

Source: Dissertation Abstracts International, Volume: 65-10, Section: B, page: 5180.