Witten non Abelian localization for Equivariant K-theory and the [Q,R] = 0 thorem / Paul-Emile Paradan, Michele Vergne.

Format:

• Book

Author/Creator:

• Paradan, Paul-Emile, author.
• Vergne, Michele, author.

Series:

• Memoirs of the American Mathematical Society ; vol. 261, no. 1257.
• Memoirs of the American Mathematical Society, 0065-9266 ; September 2019, volume 261, number 1257

Language:

English

Subjects (All):

• K-theory.
• Algebra, Homological.

Physical Description:

1 online resource (84 pages).

Edition:

1st ed.

Place of Publication:

Providence, RI : 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 the index of general spin^c Dirac operators.

Contents:

• Index theory
• K-theoretic localization
• "Quantization commutes with reduction" theorems
• Branching laws.

Notes:

• "September 2019, volume 261, number 1257 (first of 7 numbers)."
• Includes bibliographical references.
• Description based on online resource; title from PDF title page (ebrary, viewed January 6, 2020).

ISBN:

• 1-4704-5397-5
• 9781470453985

OCLC:

1130903384