Hyperbolic 4-manifolds with perfect circle-valued Morse functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2020
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| _version_ | 1866915494380961792 |
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| author | Battista, Ludovico Martelli, Bruno |
| author_facet | Battista, Ludovico Martelli, Bruno |
| contents | We exhibit some (compact and cusped) finite-volume hyperbolic four-manifolds M with perfect circle-valued Morse functions, that is circle-valued Morse functions $f\colon M \to S^1$ with only index 2 critical points. We construct in particular one example where every generic circle-valued function is homotopic to a perfect one.
An immediate consequence is the existence of infinitely many finite-volume (compact and cusped) hyperbolic 4-manifolds $M$ having a handle decomposition with bounded numbers of 1- and 3-handles, so with bounded Betti numbers $b_1(M)$, $b_3(M)$ and rank of $π_1(M)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_04997 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hyperbolic 4-manifolds with perfect circle-valued Morse functions Battista, Ludovico Martelli, Bruno Geometric Topology Differential Geometry We exhibit some (compact and cusped) finite-volume hyperbolic four-manifolds M with perfect circle-valued Morse functions, that is circle-valued Morse functions $f\colon M \to S^1$ with only index 2 critical points. We construct in particular one example where every generic circle-valued function is homotopic to a perfect one. An immediate consequence is the existence of infinitely many finite-volume (compact and cusped) hyperbolic 4-manifolds $M$ having a handle decomposition with bounded numbers of 1- and 3-handles, so with bounded Betti numbers $b_1(M)$, $b_3(M)$ and rank of $π_1(M)$. |
| title | Hyperbolic 4-manifolds with perfect circle-valued Morse functions |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2009.04997 |