The plus construction with respect to subrings of the rationals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908700783935488 |
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| author | Santiago, Guille Carrión Flores, Ramón Scherer, Jérôme |
| author_facet | Santiago, Guille Carrión Flores, Ramón Scherer, Jérôme |
| contents | We construct explicit models of universal $H \mathbb{Z}[J^{-1}]$-acyclic spaces $\mathcal M$, for any subset $J$ of the prime numbers. The corresponding nullification functors provide thus plus construction functors for ordinary homology with $\mathbb{Z}[J^{-1}]$ coefficients. Motivated by classical results about Quillen's plus construction for integral homology, we prove that the $H \mathbb{Z}[J^{-1}]$-acyclization functor and the $\mathcal M$-cellularization functor coincide. We show that the acyclization-plus construction fiber sequence is always a cofiber sequence for simply connected spaces, but almost never so when the plus construction is not simply connected, unlike in the classical case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_11839 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The plus construction with respect to subrings of the rationals Santiago, Guille Carrión Flores, Ramón Scherer, Jérôme Algebraic Topology Group Theory K-Theory and Homology 19D06, 55P60, 20F05 We construct explicit models of universal $H \mathbb{Z}[J^{-1}]$-acyclic spaces $\mathcal M$, for any subset $J$ of the prime numbers. The corresponding nullification functors provide thus plus construction functors for ordinary homology with $\mathbb{Z}[J^{-1}]$ coefficients. Motivated by classical results about Quillen's plus construction for integral homology, we prove that the $H \mathbb{Z}[J^{-1}]$-acyclization functor and the $\mathcal M$-cellularization functor coincide. We show that the acyclization-plus construction fiber sequence is always a cofiber sequence for simply connected spaces, but almost never so when the plus construction is not simply connected, unlike in the classical case. |
| title | The plus construction with respect to subrings of the rationals |
| topic | Algebraic Topology Group Theory K-Theory and Homology 19D06, 55P60, 20F05 |
| url | https://arxiv.org/abs/2502.11839 |