Guts and The Minimal Volume Orientable Hyperbolic 3-Manifold with 3 Cusps

Yue Zhang

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arXiv · 2304.09950

Guts and The Minimal Volume Orientable Hyperbolic 3-Manifold with 3 Cusps

Yue Zhang

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Abstract

The minimal volume of orientable hyperbolic manifolds with a given number of cusps has been found for $0,1,2,4$ cusps, while the minimal volume of 3-cusped orientable hyperbolic manifolds remains unknown. By using guts in sutured manifolds and pared manifolds, we are able to show that for an orientable hyperbolic 3-manifold with 3 cusps such that every second homology class is libroid, its volume is at least $5.49\ldots = 6 \times $Catalan's constant.

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Yue Zhang. 2023-04-19. Guts and The Minimal Volume Orientable Hyperbolic 3-Manifold with 3 Cusps. https://arxiv.org/abs/2304.09950

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