Stable moduli spaces of odd-dimensional manifold triads
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912662482321408 |
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| author | Fernandes, João Lobo |
| author_facet | Fernandes, João Lobo |
| contents | We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is $1$-connected. Stabilization is performed by taking boundary connected sum with $S^n \times D^{n+1}$. This is an analog of earlier work of Galatius and Randal-Williams for even-dimensional manifolds with fixed boundary, and it extends a previous result by Botvinnik and Perlmutter. As a byproduct, we obtain an analog for odd-dimensional triads of Kreck's stable diffeomorphism classification of even-dimensional manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_17986 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable moduli spaces of odd-dimensional manifold triads Fernandes, João Lobo Algebraic Topology Geometric Topology 55R40, 57S05, 57R90, 57R15, 57R56, 57R20 We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is $1$-connected. Stabilization is performed by taking boundary connected sum with $S^n \times D^{n+1}$. This is an analog of earlier work of Galatius and Randal-Williams for even-dimensional manifolds with fixed boundary, and it extends a previous result by Botvinnik and Perlmutter. As a byproduct, we obtain an analog for odd-dimensional triads of Kreck's stable diffeomorphism classification of even-dimensional manifolds. |
| title | Stable moduli spaces of odd-dimensional manifold triads |
| topic | Algebraic Topology Geometric Topology 55R40, 57S05, 57R90, 57R15, 57R56, 57R20 |
| url | https://arxiv.org/abs/2510.17986 |