PreprintCC BY 4.0arXiv
A higher categorical approach to graded bivariant K-theories for Real C*-algebras
Abstract
We present an ∞-categorical refinement of classical KK-theory and E-theory for graded, G-equivariant for a locally compact second countable group G, Real C*-algebras. As a consequence, we obtain a couple of fiber sequences connecting the different K-theory spectra, and explicitly analyse the induced endomorphisms on K0-groups. We also answer precisely some folklore questions in the area. Among other things, we show that graded KK- and E-categories are not a Dwyer-Kan localization of graded C*-algebras.
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BibTeX
@misc{datta2026higher,
title = {{A higher categorical approach to graded bivariant $K$-theories for Real $C^*$-algebras}},
author = {Anupam Datta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17060},
eprint = {2610.17060},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17060},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A higher categorical approach to graded bivariant K-theories for Real C^*-algebras
AU - Anupam Datta
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17060
UR - https://arxiv.org/abs/2610.17060
AB - We present an ∞-categorical refinement of classical KK-theory and E-theory for graded, G-equivariant for a locally compact second countable group G, Real C^*-algebras. As a consequence, we obtain a couple of fiber sequences connecting the different K-theory spectra, and explicitly analyse the induced endomorphisms on K_0-groups. We also answer precisely some folklore questions in the area. Among other things, we show that graded KK- and E-categories are not a Dwyer-Kan localization of graded C^*-algebras.
ER -