Jonathan C. Johnson

E-mail: jonathan.johnson10@okstate.edu
Office: MSCS 524
Department of Mathematics
Oklahoma State University

Applications of Heegaard Floer Homology

Heegaard Floer theory was introduced in 2001 by Ozsvath and Szabo. The theory provides a package of invariants for 3-manifolds, smooth 4-manifolds and knots. It has proved to be a powerful tool, leading to many important advances in low-dimensional topology and solutions to long-standing problems that resisted previously known methods. Glorious as it sounds, it comes with a price; it is difficult and technical. Hence, this seminar aims to study some of its applications in order to understand it a little better. Our focus is on questions about knots and surgeries.

Resources

Papers
  Eftekhary, "Heegaard Floer homology of pretzel knots" (2003)
  Ghiggini, "Knot Floer homology detects genus-one fibred knots" (2006)
  Hendricks and Manolescu, "Involutive Heegaard Floer homology" (2016)
  Livingston, "Notes on the knot concordance invariant Upsilon" (2015)
  Ni, "Knot Floer homology detects fibred knots" (2006)
  Ozsváth and Szabó, "Holomorphic disks and genus bounds" (2003)
  Ozsváth and Szabó, "Holomorphic disks and lens space surgeries" (2005)

Videos
  Jennifer Hom, PCMI Talk Series on Heegaard Floer Homology
  Yi Ni, Perspectives on Dehn Surgery Talk Series on Heegaard Floer Homology (go to the end of the page)

Notes and Exercises
  Danny Calegari, Chapter on Foliations and Floer Theories
  Jennifer Hom, Notes on Heegaard Floer Homology
  Ciprian Manolescu, "Lectures on the triangulation conjecture"
  Yi Ni, Exercises on Heegaard Floer Homology
  George Torres, Notes on Contact Topology(from Bob Gompf's class)

Books
  Yakov Eliashberg and William Thurston, Confoliations
  Ieke Moerdijk and Janez Mrčun, Introduction to Foliations and Lie Groupoids

Schedule

This seminar meets in RLM 12.166 at 2:00pm. Here's the tentative schedule for this seminar.:

September 6/13: Introduction to HF & HFK (Kai)
  Resource: Jen Hom PCMI videos Lecture 2&3

September 20: HF & Surgery (Shiyu)
  Resource: Jen Hom PCMI videos Lecture 4
  Yi Ni PoD videos is also a good source

September 27/October 4: Introduction to Taut Foliations (Cass)
  Resource: Introduction to Foliations and Lie Groupoids; Confoliations
  Also, Calegari's chapter on Foliations and Floer Theory and George's Contact Topology notes

October 11 (at noon): Pizza Seminar - Knot Concordances and HF (Ceren)

October 14: Jen is here! Go to Senior Topology and Colloquium seminars, and then dinner!

October 18/25: HF and 3-genus (Hannah)
  Resource: Ozsváth and Szabó, Holomorphic disks and genus bounds

November 1: HF and Lens Space Surgeries (Jonathan)
  Resource: Ozsváth and Szabó, Holomorphic disks and lens space surgeries

November 8: Triangulation Conjecture Seminar - Involutive Heegaard Floer Homology, part 1 (Jonathan, 11:00 on 8th floor)
  Resource: Manolescu, Lectures on the triangulation conjecture

November 15: Triangulation Conjecture Seminar - Involutive Heegaard Floer Homology, part 2 (Kai, 11:00 on 8th floor)
  Resource: Manolescu, Lectures on the triangulation conjecture

November 22: Upsilon invariant (Ceren)
  Resource: Livingston, Notes on the knot concordance invariant Upsilon