Controlled objects in left-exact $\infty$-categories and the Novikov conjecture
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866909135159689216 |
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| author | Bunke, Ulrich Cisinski, Denis-Charles Kasprowski, Daniel Winges, Christoph |
| author_facet | Bunke, Ulrich Cisinski, Denis-Charles Kasprowski, Daniel Winges, Christoph |
| contents | We associate to every $G$-bornological coarse space $X$ and every left-exact $\infty$-category with $G$-action a left-exact infinity-category of equivariant $X$-controlled objects. Postcomposing with algebraic K-theory leads to {new} equivariant coarse homology theories. This allows us to apply the injectivity results for assembly maps by Bunke, Engel, Kasprowski and Winges to the algebraic K-theory of left-exact $\infty$-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_02338 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Controlled objects in left-exact $\infty$-categories and the Novikov conjecture Bunke, Ulrich Cisinski, Denis-Charles Kasprowski, Daniel Winges, Christoph K-Theory and Homology Algebraic Topology Metric Geometry We associate to every $G$-bornological coarse space $X$ and every left-exact $\infty$-category with $G$-action a left-exact infinity-category of equivariant $X$-controlled objects. Postcomposing with algebraic K-theory leads to {new} equivariant coarse homology theories. This allows us to apply the injectivity results for assembly maps by Bunke, Engel, Kasprowski and Winges to the algebraic K-theory of left-exact $\infty$-categories. |
| title | Controlled objects in left-exact $\infty$-categories and the Novikov conjecture |
| topic | K-Theory and Homology Algebraic Topology Metric Geometry |
| url | https://arxiv.org/abs/1911.02338 |