Skip to main content

Morse Structures on Partial Open Books with Extendable Monodromy

  • 780 Accesses

Part of the MATRIX Book Series book series (MXBS,volume 1)

Abstract

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-72299-3_15
  • Chapter length: 17 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   89.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-72299-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   119.99
Price excludes VAT (USA)
Hardcover Book
USD   169.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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). http://dx.doi.org/10.1090/pspum/082/2768654

  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. Gay, D.T., Licata, J.E.: Morse structures on open books (2015). http://arxiv.org/abs/1508.05307

  4. Giroux, E.: Convexité en topologie de contact. Comment. Math. Helv. 66(4), 637–677 (1991)

    Google Scholar 

  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. 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. Honda, K., Kazez, W.H., Matić, G.: The contact invariant in sutured Floer homology. Invent. Math. 176(3), 637–676 (2009). http://dx.doi.org/10.1007/s00222-008-0173-3

  8. Juhász, A.: Holomorphic discs and sutured manifolds. Algebr. Geom. Topol. 6, 1429–1457 (2006) (electronic)

    Google Scholar 

  9. Lipshitz, R., Ozsvath, P., Thurston, D.: Bordered Heegaard Floer homology: invariance and pairing (2008). http://arxiv.org/abs/0810.0687

  10. Mathews, D.V.: Strand algebras and contact categories (2016). http://arxiv.org/abs/1608.02710

  11. Torisu, I.: Convex contact structures and fibered links in 3-manifolds. Int. Math. Res. Not. (9), 441–454 (2000). http://dx.doi.org/10.1155/S1073792800000246

  12. Zarev, R.: Bordered Floer homology for sutured manifolds (2009). http://arxiv.org/abs/0908.1106

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Joan E. Licata .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Licata, J.E., Mathews, D.V. (2018). Morse Structures on Partial Open Books with Extendable Monodromy. In: de Gier, J., Praeger, C., Tao, T. (eds) 2016 MATRIX Annals. MATRIX Book Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-72299-3_15

Download citation