Hyperbolic 4-manifolds with perfect circle-valued Morse functions

Ludovico Battista; Bruno Martelli

doi:10.1090/tran/8542

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arXiv · 2009.04997

Hyperbolic 4-manifolds with perfect circle-valued Morse functions

Ludovico Battista·Bruno Martelli

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Abstract

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 $\pi_1(M)$.

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BibTeX RIS

Ludovico Battista, Bruno Martelli. 2020-09-10. Hyperbolic 4-manifolds with perfect circle-valued Morse functions. https://doi.org/10.1090/tran/8542

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