Special moves for open book decompositions of 3-manifolds

Riccardo Piergallini; Daniele Zuddas

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arXiv · 1801.01858

Special moves for open book decompositions of 3-manifolds

Riccardo Piergallini·Daniele Zuddas

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Abstract

We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer's twisting, which is presented in two different (but stably equivalent) forms. Our approach relies on 4-dimensional Lefschetz fibrations, and on 3-dimensional contact topology, via the Giroux-Goodman stable equivalence theorem for open book decompositions representing homologous contact structures.

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Riccardo Piergallini, Daniele Zuddas. 2018-01-05. Special moves for open book decompositions of 3-manifolds. https://arxiv.org/abs/1801.01858

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