Spring 2017: Topology reading seminar

Time and place: We will meet on Tuesday, 1-2:30pm, in room Math 622 unless noted otherwise.

Topic: Embedded surfaces in 4-manifolds

Mailing list: If you would like to (un)subscribe to the mailing list, please send an e-mail to alishahi@math.columbia.edu.

Date Speaker Title
Jan 24 Mike Wong Diagrams of knotted surfaces
Jan 31 Akram Alishahi Deform spinning, Ribbon surfaces and connected sum
Feb 7 Nathan Dowlin Constructions of knotted surfaces(2)
Feb 14 Mike Wong The exterior of a knotted surface and its fundamental group
Feb 21 Zhechi Cheng Topological Invariants of knotted surfaces(2)
Feb 28 James Cornish
Mar 7
Mar 14 No talk: Spring break
Mar 21 Nathan Dowlin arXiv:1507.08370
Mar 28 Akram Alishahi arXiv:1504.04086
Apr 4 James Cornish Cancelled
Apr 11 James Cornish arXiv:1310.8516
Apr 18 Mike Wong arXiv:1509.02738
Apr 25 Zhechi Cheng arXiv:1602.08821
May 2 Adam Levine Heegaard Floer invariants for homology S^1xS^3s


1- S. Carter, S. Kamada, M. Saito, Surfaces in 4-space
2- I. Baykur, N. Sunukjian, Knotted surfaces in 4-manifolds and stabilizations: arXiv:1504.04086 (Akram)
3- A. Juhasz, M. Marengon, Concordance maps in knot Floer homology: arXiv:1509.02738 (Mike)
4- J. Meier, A. Zupan: Bridge trisections of knotted surfaces in S4: arXiv:1507.08370(Nate)
5- I. Gessel, A. Levine, D. Ruberman, S. Strle: Non-orientable surfaces in homology cobordisms: arXiv:1310.8516 (James)
6- P. Kronheimer: Embedded surfaces and gauge theory in three and four dimensions
7- G. Rizell, E. Goodman, A. Ivrii, Lagrangian isotopy of tori in S2×S2 and ℂP2: arXiv:1602.08821 (Zhechi)

May 2: Adam Levine "Heegaard Floer invariants for homology S^1xS^3s"

Abstract: Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented 4-manifold X with the homology of S^1 \times S^3. Specifically, we show that for any smoothly embedded 3-manifold Y representing a generator of H_3(X), a suitable version of the Heegaard Floer d invariant of Y, defined using twisted coefficients, is a diffeomorphism invariant of X.