Morse Structures on Partial Open Books with Extendable Monodromy

  • Joan E. LicataEmail author
  • Daniel V. Mathews
Part of the MATRIX Book Series book series (MXBS, volume 1)


The first author in recent work with D. Gay developed the notion of a Morse structure on an open book as a tool for studying closed contact 3-manifolds. We extend the notion of Morse structure to extendable partial open books in order to study contact 3-manifolds with convex boundary.


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The authors would like to acknowledge the support and hospitality of MATRIX during the workshop Quantum Invariants and Low-Dimensional Topology. The second author is supported by Australian Research Council grant DP160103085.


  1. 1.
    Etgü, T., Ozbagci, B.: On the relative Giroux correspondence. In: Low-Dimensional and Symplectic Topology. Proceedings of Symposia in Pure Mathematics, vol. 82, pp. 65–78. American Mathematical Society, Providence, RI (2011).
  2. 2.
    Farb, B., Margalit, D.: A Primer on Mapping Class Groups. Princeton Mathematical Series, vol. 49. Princeton University Press, Princeton, NJ (2012)Google Scholar
  3. 3.
    Gay, D.T., Licata, J.E.: Morse structures on open books (2015).
  4. 4.
    Giroux, E.: Convexité en topologie de contact. Comment. Math. Helv. 66(4), 637–677 (1991)Google Scholar
  5. 5.
    Giroux, E.: Structures de contact en dimension trois et bifurcations des feuilletages de surfaces. Invent. Math. 141(3), 615–689 (2000)Google Scholar
  6. 6.
    Giroux, E.: Géométrie de contact: de la dimension trois vers les dimensions supérieures. In: Proceedings of the International Congress of Mathematicians, (Beijing, 2002), vol. II, pp. 405–414. Higher Education Press, Beijing (2002)Google Scholar
  7. 7.
    Honda, K., Kazez, W.H., Matić, G.: The contact invariant in sutured Floer homology. Invent. Math. 176(3), 637–676 (2009).
  8. 8.
    Juhász, A.: Holomorphic discs and sutured manifolds. Algebr. Geom. Topol. 6, 1429–1457 (2006) (electronic)Google Scholar
  9. 9.
    Lipshitz, R., Ozsvath, P., Thurston, D.: Bordered Heegaard Floer homology: invariance and pairing (2008).
  10. 10.
    Mathews, D.V.: Strand algebras and contact categories (2016).
  11. 11.
    Torisu, I.: Convex contact structures and fibered links in 3-manifolds. Int. Math. Res. Not. (9), 441–454 (2000).
  12. 12.
    Zarev, R.: Bordered Floer homology for sutured manifolds (2009).

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical Sciences InstituteThe Australian National UniversityCanberraAustralia
  2. 2.School of Mathematical SciencesMonash UniversityClaytonAustralia

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