Periodic surface homeomorphisms and contact structures
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.
Abstract
In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.
참고문헌 (16)
- K. L. Baker, "Cabling, contact structures and mapping class monoids", J. Differential Geom, 90(1), pp.1~80 (2012)
- J. A. Baldwin, "Admissible transverse surgery does not preserve tightness", Math. Ann, 357(2), pp.441~468 (2013)[DOI]
- V. Colin, "Reeb vector fields and open book decompositions", J. Eur. Math. Soc. (JEMS), 15(2), pp.443~507 (2013)[DOI]
- N. K. Dhanwani, "Factoring periodic maps into Dehn twists", J. Pure Appl. Algebra, 227(1), pp.33~ (2023)[DOI]
- J. Gilman, "Structures of elliptic irreducible subgroups of the modular group", Proc. London Math. Soc. (3), 47(1), pp.27~42 (1983)[DOI]
- E. Giroux, "G´eom´etrie de contact: de la dimension trois vers les dimensions sup´erieures", Proceedings of the International Congress of Mathematicians, 2, pp.405~414 (2002), Higher Ed. Press
- K. Honda, "Right-veering diffeomorphisms of compact surfaces with boundary. II", Geom. Topol, 12(4), pp.2057~2094 (2008)[DOI]
- S. P. Kerckhoff, "The Nielsen realization problem", Ann. of Math. (2), 117(2), pp.235~265 (1983)[DOI]
- A. Loi, "Compact Stein surfaces with boundary as branched covers of B4", Invent. Math, 143(2), pp.325~348 (2001)[DOI]
- A. Mori, "A note on Thurston-Winkelnkemper’s construction of contact forms on 3-manifolds", Osaka J. Math, 39(1), pp.1~11 (2002)
- S. Parsad, "Geometric realizations of cyclic actions on surfaces", J. Topol. Anal, 11(4), pp.929~964 (2019)[DOI]
- F. Quinn, "Open book decompositions, and the bordism of automorphisms", Topology, 18(1), pp.55~73 (1979)[DOI]
- K. Rajeevsarathy, "Roots of Dehn twists about multicurves", Glasg. Math. J, 60(3), pp.555~583 (2018)[DOI]
- W. P. Thurston, "On the geometry and dynamics of diffeomorphisms of surfaces", Bull. Amer. Math. Soc. (N.S.), 19(2), pp.417~431 (1988)[DOI]
- W. P. Thurston, "On the existence of contact forms", Proc. Amer. Math. Soc, 52, pp.345~347 (1975)[DOI]
- H. E. Winkelnkemper, "Manifolds as open books", Bull. Amer. Math. Soc, 79, pp.45~51 (1973)[DOI]