Boundary of free products of metric spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913230944731136 |
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| author | Fukaya, Tomohiro Matsuka, Takumi |
| author_facet | Fukaya, Tomohiro Matsuka, Takumi |
| contents | In this paper, we compute (co)homologies of ideal boundaries of free products of geodesic coarsely convex spaces in terms of those of each of the components. The (co)homology theories we consider are, $K$-theory, Alexander-Spanier cohomology, $K$-homology, and Steenrod homology. These computations led to the computation of $K$-theory of the Roe algebra of free products of geodesic coarsely convex spaces via the coarse Baum-Connes conjecture. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_06862 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary of free products of metric spaces Fukaya, Tomohiro Matsuka, Takumi Metric Geometry Algebraic Topology Primary 51F30, Secondary 20F65, 58B34 In this paper, we compute (co)homologies of ideal boundaries of free products of geodesic coarsely convex spaces in terms of those of each of the components. The (co)homology theories we consider are, $K$-theory, Alexander-Spanier cohomology, $K$-homology, and Steenrod homology. These computations led to the computation of $K$-theory of the Roe algebra of free products of geodesic coarsely convex spaces via the coarse Baum-Connes conjecture. |
| title | Boundary of free products of metric spaces |
| topic | Metric Geometry Algebraic Topology Primary 51F30, Secondary 20F65, 58B34 |
| url | https://arxiv.org/abs/2402.06862 |