Quotients of tangential $k$-blocks

The K-theory of Abelian Symplectic Quotients

Let T be a compact torus and (M,ω) a Hamiltonian T -space. In a previous paper, the authors showed that the T -equivariant K-theory of the manifold M surjects onto the ordinary integral K-theory of the symplectic quotient M//T , under certain technical conditions on the moment map. In this paper, we use equivariant Morse theory to give a method for computing theK-theory of M//T by obtaining an ...

The K-theory of symplectic quotients

Let G be a compact connected Lie group, and (M,ω) a compact Hamiltonian Gspace with moment map μ. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the original manifold M , under certain technical conditions on μ. This result is a natural K-theoretic analogue of the Kirwan surjectivity theorem in symplectic geomet...

Hyper - K Ahler Quotients of Solvable Lie Groupsm

Quotients of Milnor K-rings, Orderings, and Valuations

We define and study the Milnor K-ring of a field F modulo a subgroup of the multiplicative group of F . We compute it in several arithmetical situations, and study the reflection of orderings and valuations in this ring. Introduction Let F be a field and let F× be its multiplicative group. The Milnor K-ring K ∗ (F ) of F is the tensor (graded) algebra of the Z-module F× modulo the homogenous id...

The Full Orbifold K-theory of Abelian Symplectic Quotients

In their 2007 paper, Jarvis, Kaufmann, and Kimura defined the full orbifold K-theory of an orbifold X, analogous to the Chen-Ruan orbifold cohomology of X in that it uses the obstruction bundle as a quantum correction to the multiplicative structure. We give an explicit algorithm for the computation of this orbifold invariant in the case when X arises as an abelian symplectic quotient. Our meth...