Abstract
We study –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.
Citation
Tetsuya Ito. Keiko Kawamuro. "Operations on open book foliations." Algebr. Geom. Topol. 14 (5) 2983 - 3020, 2014. https://doi.org/10.2140/agt.2014.14.2983
Information