Operations on open book foliations

Ito, Tetsuya¹ ; Kawamuro, Keiko²

¹Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
²Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 2983-3020

Résumé

We study b–arc foliation changes and exchange moves of open book foliations which generalize the corresponding operations in braid foliation theory. We also define a bypass move as an analogue of Honda’s bypass attachment operation.

As applications, we study how open book foliations change under a stabilization of the open book. We also generalize Birman–Menasco’s split/composite braid theorem: we show that closed braid representatives of a split (resp. composite) link in a certain open book can be converted to a split (resp. composite) closed braid by applying exchange moves finitely many times.

Détail

DOI : 10.2140/agt.2014.14.2983

Classification : 57M27
Keywords: open book foliation, exchange move, bypass move, stabilization

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