Volume 19 (2015)

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ISSN (electronic): 1464-8997
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Interactions between low-dimensional topology and mapping class groups

Editors: R Inanc Baykur, John Etnyre and Ursula Hamenstädt

There has been a long history of rich and subtle connections between low dimensional topology, mapping class groups and geometric group theory. From July 1 to July 5, 2013, the conference “Interactions between low dimensional topology and mapping class groups” held at the Max Planck Institute for Mathematics in Bonn highlighted these diverse connections, and fostered new and unexpected collaborations between researchers in these areas.

The proceedings for this conference aims to further draw attention to the beautiful mathematics emerging from diverse interactions between these areas. The articles collected in this volume, in addition to gathering new results, also contain expositions and surveys of the latest developments in various active areas of research at the interface of mapping class groups of surfaces and the topology and geometry of 3– and 4–dimensional manifolds. Many open problems and new directions for research are discussed.

Details on the conference, including the schedule, list of participants, and videos of the main lectures can be found at the conference webpage.

Sections of surface bundles

Jonathan A Hillman

Approximating $C^{1,0}$–foliations

William H Kazez and Rachel Roberts

On the topology of fillings of contact $3$–manifolds

Burak Ozbagci

Universal Lefschetz fibrations and Lefschetz cobordisms

Daniele Zuddas

Open book decompositions versus prime factorizations of closed, oriented $3$–manifolds

Paolo Ghiggini and Paolo Lisca

On the self-linking number of transverse links

Tetsuya Ito and Keiko Kawamuro

Symplectic $4$–manifolds, Stein domains, Seiberg–Witten theory and mapping class groups

András I Stipsicz

Decision problems for $3$–manifolds and their fundamental groups

Matthias Aschenbrenner, Stefan Friedl and Henry Wilton

Charts, signatures, and stabilizations of Lefschetz fibrations

Hisaaki Endo, Isao Hasegawa, Seiichi Kamada and Kokoro Tanaka

Broken Lefschetz fibrations and mapping class groups

R İnanç Baykur and Kenta Hayano

Detecting tightness via open book decompositions

Andy Wand

Monoids in the mapping class group

John B Etnyre and Jeremy Van Horn-Morris

Some $3$–dimensional transverse $\mathbb{C}$–links (Constructions of higher-dimensional $\mathbb{C}$–links, I)

Lee Rudolph