Witten non abelian localization for equivariant K-theory, and the [Q, R] = 0 theorem / Paul-Emile Paradan, Michéle Vergne.

Format:

Book

Author/Creator:

Paradan, Paul-Emile, author.

Vergne, Michèle, author.

Series:

Memoirs of the American Mathematical Society ; 0065-9266 no. 1257.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1257

Language:

English

Subjects (All):

Non-Abelian groups.

K-theory.

Physical Description:

v, 71 pages ; 26 cm.

Place of Publication:

Providence : American Mathematical Society, [2019]

Summary:

The purpose of the present memoir is two-fold. First, the authors obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, the authors deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, the authors use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case and obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplicities of index of general spin(c) Dirac operations.

Notes:

"September 2019; Volume 261; number 1257 (first of 7 numbers)"--Cover.

Includes bibliographical references (pages 69-71)

ISBN:

9781470435226

1470435225

OCLC:

1109434469