Planar open books, monodromy factorizations and symplectic fillings

Plamenevskaya, Olga; Horn-Morris, Jeremy Van

doi:10.2140/gt.2010.14.2077

Cited by 54 publications

(72 citation statements)

References 24 publications

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“…1 As Burak Ozbagci kindly pointed out to us, this generalized lantern relation is equivalent to a relation obtained by Plamenevskaya and Van Horn-Morris in [17].…”

Section: Commutator Length Of the Dehn Twist About A Boundary Componentmentioning

confidence: 73%

Sections of surface bundles and Lefschetz fibrations

Baykur

Korkmaz

Monden

2013

Trans. Amer. Math. Soc.

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Abstract. We investigate the possible self-intersection numbers for sections of surface bundles and Lefschetz fibrations over surfaces. When the fiber genus g and the base genus h are positive, we prove that the adjunction bound 2h − 2 is the only universal bound on the self-intersection number of a section of any such genus g bundle and fibration. As a side result, in the mapping class group of a surface with boundary, we calculate the precise value of the commutator lengths of all powers of a Dehn twist about a boundary component, concluding that the stable commutator length of such a Dehn twist is 1/2. We furthermore prove that there is no upper bound on the number of critical points of genus-g Lefschetz fibrations over surfaces with positive genera admitting sections of maximal self-intersection, for g ≥ 2.

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“…1 As Burak Ozbagci kindly pointed out to us, this generalized lantern relation is equivalent to a relation obtained by Plamenevskaya and Van Horn-Morris in [17].…”

Section: Commutator Length Of the Dehn Twist About A Boundary Componentmentioning

confidence: 73%

Sections of surface bundles and Lefschetz fibrations

Baykur

Korkmaz

Monden

2013

Trans. Amer. Math. Soc.

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“…Ohta and Ono [20,21] determined the diffeomorphism types of symplectic fillings of links of simple elliptic and simple singularities endowed with their natural contact structures. Stein fillings up to diffeomorphisms were classified by the second author [12] for all lens spaces with their standard contact structures, by Plamenevskaya-Van Horn-Morris [22] on L(p, 1) with other contact structures and by Starkston [23] for certain contact Seifert fibered 3-manifolds. In this paper, we study Stein and symplectic fillings of infinitely many contact torus bundles over the circle.…”

Section: Introductionmentioning

confidence: 99%

On Stein fillings of contact torus bundles

Golla

Lisca

2015

Bulletin of London Math Soc

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We consider a large family MJX-tex-caligraphicscriptF of torus bundles over the circle, and we use recent work of Li–Mak to construct, on each Y∈F, a Stein fillable contact structure ξY. We prove that (i) each Stein filling of (Y,ξY) has vanishing first Chern class and first Betti number, (ii) if Y∈F is elliptic, then all Stein fillings of (Y,ξY) are pairwise diffeomorphic and (iii) if Y∈F is parabolic or hyperbolic, then all Stein fillings of (Y,ξY) share the same Betti numbers and fall into finitely many diffeomorphism classes. Moreover, for infinitely many hyperbolic torus bundles Y∈F we exhibit non‐homotopy equivalent Stein fillings of (Y,ξY).

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“…Course n o III-Complex singularities and contact topology As explained by Cieliebak and Eliashberg [33,Theorem 16.10], this theorem was strengthened by Plamenevskaya and Van Horn Morris [159] and Hind [77].…”

Section: Iii-64mentioning

confidence: 95%

Complex singularities and contact topology

Popescu-Pampu¹

2017

Winter Braids Lecture Notes

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This text is a greatly expanded version of the mini-course I gave during the school Winter Braids VI organized in Lille between 22-25 February 2016. It is an introduction to the study of interactions between singularity theory of complex analytic varieties and contact topology. I concentrate on the relation between the smoothings of singularities and the Stein fillings of their contact boundaries. I tried to explain basic intuitions and facts in both fields, for the sake of the readers who are not accustomed with one of them.

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Planar open books, monodromy factorizations and symplectic fillings

Cited by 54 publications

References 24 publications

Sections of surface bundles and Lefschetz fibrations

Sections of surface bundles and Lefschetz fibrations

On Stein fillings of contact torus bundles

Complex singularities and contact topology

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