Description: Applications of Seiberg-Witten theory to various problems in geometry and topology of 3- and 4-manifolds, with ramifications to algebraic and symplectic geometry, contact manifolds, Floer homology and more refined invariants.

Announcements

• We will have two guest speakers who have kindly agreed to talk on the following topics:
  • Cumrun Vafa on the physics of Seiberg-Witten theory, April 17, 2008.
  • Clifford Taubes on vortex equations, April 29, 2008.
  If you plan to attend one of these talks and you have not registered in the course, please e-mail me by April 13 (respectively April 27), as class space is limited.

• Steven Sivek will talk about the work of Furuta-Bauer on April 22.
  Meanwhile, have a look at Seiberg-Witten theory and $Z/2^p$ actions on spin 4-manifolds by Jim Bryan.

• The text would possibly be the recent book by Kronheimer and Mrowka on monopoles and three-manifolds, published by the Cambridge University Press.
  ISBN-10: 052188022X

Miscellaneous References

• Peter Ozsváth and Zoltán Szabó, An introduction to Heegaard Floer homology.
• Yi-Jen Lee, Heegaard Splittings and Seiberg-Witten monopoles, arXiv:math/0409536v2.
• Clifford Henry Taubes, The Seiberg-Witten equations and the Weinstein conjecture, Geometry & Topology 11 (2007) 2117--2202; DOI: 10.2140/gt.2007.11.2117.
  (There are shorter expositions as well, please let me know if you are interested.)
• Robert Friedman and John W. Morgan, Algebraic surfaces and Seiberg-Witten invariants, arXiv:alg-geom/9502026v2,
  as well as Obstruction bundles, semiregularity, and Seiberg-Witten invariants, arXiv:alg-geom/9509007v1.
• Pedram Safari, Gluing Seiberg-Witten Monopoles, Comm. An. Geom, vol. 13, no. 4 (Oct. 2005), 697-725.
• Vladimir Turaev, Torsion invariants of Spin^c-structures on 3-manifolds, Math. Research Letters, Volume 4, Issue 5, September 1997, pp. 679-695.