# Reeb vector fields and open book decompositions

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 2, page 443-507
- ISSN: 1435-9855

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topColin, Vincent, and Honda, Ko. "Reeb vector fields and open book decompositions." Journal of the European Mathematical Society 015.2 (2013): 443-507. <http://eudml.org/doc/277710>.

@article{Colin2013,

abstract = {We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux.We study two cases: when the monodromy map of the compatible open book is periodic and when it is pseudo-Anosov. For an open book with periodic monodromy, we verify the Weinstein conjecture. In the case of an open book with pseudo-Anosov monodromy, suppose the boundary of a page of the open book is connected and the fractional Dehn twist coefficient $c$ equals $k=n$, where $n$ is the number of prongs along the boundary. If $k\ge 2$, then there is a well-defined linearized contact homology group. If $k\ge 3$, then the linearized contact homology is exponentially growing with respect to the action, and every Reeb vector field of the corresponding contact structure admits an infinite number of simple periodic orbits.},

author = {Colin, Vincent, Honda, Ko},

journal = {Journal of the European Mathematical Society},

keywords = {tight; contact structure; open book decomposition; mapping class group; Reeb dynamics; pseudo-Anosov; contact homology; tight; contact structure; open book decomposition; mapping class group; Reeb dynamics; pseudo-Anosov; contact homology},

language = {eng},

number = {2},

pages = {443-507},

publisher = {European Mathematical Society Publishing House},

title = {Reeb vector fields and open book decompositions},

url = {http://eudml.org/doc/277710},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Colin, Vincent

AU - Honda, Ko

TI - Reeb vector fields and open book decompositions

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 2

SP - 443

EP - 507

AB - We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux.We study two cases: when the monodromy map of the compatible open book is periodic and when it is pseudo-Anosov. For an open book with periodic monodromy, we verify the Weinstein conjecture. In the case of an open book with pseudo-Anosov monodromy, suppose the boundary of a page of the open book is connected and the fractional Dehn twist coefficient $c$ equals $k=n$, where $n$ is the number of prongs along the boundary. If $k\ge 2$, then there is a well-defined linearized contact homology group. If $k\ge 3$, then the linearized contact homology is exponentially growing with respect to the action, and every Reeb vector field of the corresponding contact structure admits an infinite number of simple periodic orbits.

LA - eng

KW - tight; contact structure; open book decomposition; mapping class group; Reeb dynamics; pseudo-Anosov; contact homology; tight; contact structure; open book decomposition; mapping class group; Reeb dynamics; pseudo-Anosov; contact homology

UR - http://eudml.org/doc/277710

ER -

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