TY - CHAP
T1 - Contact open books and symplectic lefschetz fibrations (survey)
AU - Acu, Bahar
N1 - Publisher Copyright:
© The Author(s) and the Association for Women in Mathematics 2020.
PY - 2020
Y1 - 2020
N2 - This note surveys two fundamental tools that unlock several topological properties of contact and symplectic manifolds; open book decompositions and Lefschetz fibrations. In particular, we will focus on planar contact manifolds, those that correspond to an open book decomposition with genus zero pages, and provide some fundamental results concerning planar open book decompositions and planar Lefschetz fibrations. We also introduce a higher-dimensional notion of planarity, iterated planarity as in [2], and present an exposition of generalizations of some of those results to higher dimensions.
AB - This note surveys two fundamental tools that unlock several topological properties of contact and symplectic manifolds; open book decompositions and Lefschetz fibrations. In particular, we will focus on planar contact manifolds, those that correspond to an open book decomposition with genus zero pages, and provide some fundamental results concerning planar open book decompositions and planar Lefschetz fibrations. We also introduce a higher-dimensional notion of planarity, iterated planarity as in [2], and present an exposition of generalizations of some of those results to higher dimensions.
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U2 - 10.1007/978-3-030-42687-3_18
DO - 10.1007/978-3-030-42687-3_18
M3 - Chapter
AN - SCOPUS:85089532673
T3 - Association for Women in Mathematics Series
SP - 273
EP - 285
BT - Association for Women in Mathematics Series
PB - Springer
ER -