Equivariant $KK$-theory and model categories
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913903435317248 |
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| author | Datta, Anupam Joachim, Michael |
| author_facet | Datta, Anupam Joachim, Michael |
| contents | We cast Kasparov's equivariant KK-theory in the framework of model categories. We obtain a stable model structure on a certain category of locally multiplicative convex $G$-$C^*$-algebras, which naturally contains the stable $\infty$-category $KK^G_{\operatorname{sep}}$ as described by Bunke, Engel, Land (\cite{BEL}). Non-equivariantly, $KK$-theory was studied using model categories by Joachim-Johnson (\cite{MJ}). We generalize their ideas in the equivariant case, and also fix some critical errors that their work had. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16238 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant $KK$-theory and model categories Datta, Anupam Joachim, Michael K-Theory and Homology Algebraic Topology Operator Algebras We cast Kasparov's equivariant KK-theory in the framework of model categories. We obtain a stable model structure on a certain category of locally multiplicative convex $G$-$C^*$-algebras, which naturally contains the stable $\infty$-category $KK^G_{\operatorname{sep}}$ as described by Bunke, Engel, Land (\cite{BEL}). Non-equivariantly, $KK$-theory was studied using model categories by Joachim-Johnson (\cite{MJ}). We generalize their ideas in the equivariant case, and also fix some critical errors that their work had. |
| title | Equivariant $KK$-theory and model categories |
| topic | K-Theory and Homology Algebraic Topology Operator Algebras |
| url | https://arxiv.org/abs/2506.16238 |