A KK-theoretic perspective of quantization commutes with reduction
K-Theory and Homology
2025-09-08 v2 Differential Geometry
Operator Algebras
Abstract
We reframe Paradan-Vergne's approach to quantization commutes with reduction in KK-theory through a recent formalism introduced by Kasparov, focusing more especially the index theoretic parts that lead to their "Witten non-abelian localization formula". While our method uses the same ingredients as their's in spirit, interesting conceptual simplifications occur, and the relationship to the Ma-Tian-Zhang analytic approach becomes quite transparent.
Cite
@article{arxiv.2011.00643,
title = {A KK-theoretic perspective of quantization commutes with reduction},
author = {Rudy Rodsphon},
journal= {arXiv preprint arXiv:2011.00643},
year = {2025}
}
Comments
14 pages, minor changes