Geodesic
Filtering the Heegaard Floer contact invariant
Kutluhan, Çağatay1 ; Matić, Gordana2 ; Van Horn-Morris, Jeremy3 ; Wand, Andy4
1 Department of Mathematics, University at Buffalo, Buffalo, NY, United States
2 Department of Mathematics, University of Georgia, Athens, GA, United States
3 Department of Mathematics, University of Arkansas, Fayetteville, AR, United States
4 School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom
Geometry & topology, Tome 27 (2023) no. 6, pp. 2181-2236 Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

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We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set ℤ≥0 ∪{∞}. It is zero for overtwisted contact structures, ∞ for Stein-fillable contact structures, nondecreasing under Legendrian surgery, and computable from any supporting open book decomposition. As an application, we give an easily computable obstruction to Stein-fillability on closed contact 3–manifolds with nonvanishing Ozsváth–Szabó contact class.

DOI : 10.2140/gt.2023.27.2181
Classification : 57R17, 57R58
Keywords: Heegaard Floer homology, contact structure

Kutluhan, Çağatay 1 ; Matić, Gordana 2 ; Van Horn-Morris, Jeremy 3 ; Wand, Andy 4

1 Department of Mathematics, University at Buffalo, Buffalo, NY, United States
2 Department of Mathematics, University of Georgia, Athens, GA, United States
3 Department of Mathematics, University of Arkansas, Fayetteville, AR, United States
4 School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom 
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Kutluhan, Çağatay; Matić, Gordana; Van Horn-Morris, Jeremy; Wand, Andy. Filtering the Heegaard Floer contact invariant. Geometry & topology, Tome 27 (2023) no. 6, pp. 2181-2236. doi: 10.2140/gt.2023.27.2181

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