Knotted surfaces in 4-manifoldsOctober 26-28, 2018, University of Massachusetts, Amherst, MA
Organizing CommitteeR. Inanc Baykur (UMass Amherst), Weimin Chen (UMass Amherst) and Daniel Ruberman (Brandeis University)
The aim of this 3-day conference is to bring together active researchers in knotted surfaces in 4-manifolds, ranging from leading experts to recent PhDs and graduate students, and provide a panorama of the field through a variety of talks and discussion sessions. The talks will start at 2:30 Friday afternoon and finish by 1pm Sunday to accommodate participant travel.
Registration and support
[Funding applications are now closed.]
Funding is available for conference participation. Support requests should be made at the registration link by September 14, 2018. We particularly encourage graduate students and recent PhDs to apply. For full consideration, junior participants should also have a reference letter e-mailed to [baykur at math dot umass dot edu] by the funding request deadline.
We have reserved rooms for all the invited speakers and participants coming from outside of Western Massachusetts at the UMass Hotel and Conference Center. Please provide your planned dates of stay and accommodation preferences at the registration link above. With very few exceptions, all the rooms are reserved for the nights of Friday, October 26 and Saturday, October 27, so please plan your travel accordingly. Further inquiries regarding accommodation should be made to [wchen at math dot umass dot edu].
This event is sponsored by the National Science Foundation Grant DMS-1522633.
The closest airport to Amherst is the Bradley (Hartford/Springfield) Airport, and there are shuttle services from/to UMass Amherst. The second major airport in the area is the Logan (Boston) Airport (1,5-2hrs distance), which however requires an additional bus commute between Boston and Amherst. Greyhound buses serve between Amherst and many other locations such as Boston and New York.
Friday, October 26
2:00 - 2:30pm Registration
2:30 - 3:30pm Lambert-Cole
3:30 - 4:00pm REFRESHMENTS
4:00 - 5:00pm Sunukjian
5:15 - 6:45pm Discussion
Saturday, October 27
9:30 - 10:30am Gabai
10:30 - 10:45am TEA
10:45 - 11:45am Schwartz
12:00 - 1:00pm Yasui
2:30 - 3:30pm Suciu
3:30 - 4:00pm REFRESHMENTS
4:00 - 5:00pm Starkston
5:15 - 6:45pm Discussion
Sunday, October 28
9:30 - 10:30am Hedden
10:30 - 10:45am TEA
10:45 - 11:45am Zemke
12:00 - 1:00pm Miller
All talks and the discussion sessions will be held at Lederle Graduate Research Tower, Room 1634. Tea and refreshments will be served in the lounge area next to LGRT 1634.
Titles and abstracts
The general 4-dimensional light bulb theorem
We discuss the theorem that in a compact 4-manifold that has no 2-torsion, homotopy implies smooth isotopy for smooth embedded 2-spheres with a common embedded transverse sphere. By transverse sphere we mean a sphere with trivial normal bundle that intersects each of the other spheres transversely exactly once.
Satellites of infinite rank in the smooth concordance group
I'll discuss the way satellite operations act on the concordance group, and raise some questions and conjectures. In particular, I'll conjecture that satellite operations are either constant or have infinite rank, and reduce this to the difficult case of winding number zero satellites. I'll then talk about how to use SO(3) gauge theory to provide a general criterion sufficient for the image of a satellite operation to generate an infinite rank subgroup of smooth concordance, and use this to address the winding zero case. This is joint work with Juanita Pinzon-Caicedo.
Bridge trisections and the Thom conjecture
The classical degree-genus formula computes the genus of a nonsingular algebraic curve in the complex projective plane. The well-known Thom conjecture posits that this is a lower bound on the genus of smoothly embedded, oriented and connected surface in CP^2. The conjecture was first proved twenty-five years ago by Kronheimer and Mrowka, using Seiberg-Witten invariants. In this talk, we will describe a new proof of the conjecture that combines contact geometry with the novel theory of bridge trisections of knotted surfaces. Notably, the proof completely avoids any gauge theory or pseudoholomorphic curve techniques.
Trisections of surface complements and surgery on RP^2s
A relative trisection is a decomposition of a 4-manifold with boundary which induces an open book on the boundary. Two relative trisections can only be glued if they induce the same open book (with opposite orientation). I will show how to relatively trisect the complement of a surface S in a 4-manifold X. When S is an RP^2 of Euler number +2 or -2, we can control the resulting open book so that we may perform surgery (a "Price twist") on X along S. In particular, when X=S^4, this yields a trisected homotopy 4-sphere. This work is joint with Seungwon Kim.
Using 2-torsion to obstruct topological isotopy
It is well known that two knots in S^3 are ambiently isotopic if and only if there is an orientation preserving automorphism of S^3 carrying one knot to the other. In this talk, we will examine a family of smooth 4-manifolds in which the analogue of this fact does not hold, i.e. each manifold contains a pair of smoothly embedded, homotopic 2-spheres that are related by a diffeomorphism, but not smoothly isotopic. In particular, the presence of 2-torsion in the fundamental groups of these 4-manifolds can be used to obstruct even a topological isotopy between the 2-spheres; this shows that Gabai's recent ``4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis.
Symplectic isotopy problems
We will discuss some problems and results about symplectic surfaces in 4-manifolds, particularly in the complex projective plane. The main question is to classify symplectic surfaces up to symplectic isotopy. If the surface has singularities, we restrict the isotopies to the class of surfaces with the same model singularities.
On the topology of complex line arrangements
I will discuss some recent advances in our understanding of the multiple connections between the combinatorics of an arrangement of complex hyperplanes, the topology of its complement and boundary manifold, and the monodromy of its Milnor fibration.
Smoothly knotted, topologically trivial tori
Surfaces in a 4-manifold can be topologically isotopic, but not smoothly isotopic. In this talk, we will discuss a method for constructing such "exotic" embeddings of tori. The novel feature of this construction is that our tori are topologically trivial (in the sense that they bound a topologically embedded solid torus in the 4-manifold), but smoothly non-trivial. These examples can be constructed in any elliptic surface (among other 4-manifold), and are examples of surfaces that are not ribbon, but are stabily ribbon. This is joint work with Neil Hoffman.
Minimal genus functions and smooth structures of 4-manifolds
We discuss applications of minimal genus functions of 4-manifolds to their smooth structures. We first briefly review methods for distinguishing smooth structures of 4-manifolds by the functions. We then focus on a question whether all exotic smooth structures of a compact 4-manifold can be generated by twisting a fixed compact submanifold, and we give a partial negative answer by introducing an invariant of smooth structures determined by minimal genus functions.
The stabilization distance and link Floer homology
Given a knot K in S^3, we consider the set of oriented surfaces in B^4 which bound K. A natural question is how many stabilizations and destabilizations one must perform to move from one surface to another. In this talk, we consider a metric on the set of surfaces bounding K, which is based on how many times one must stabilize or destabilize to move from one surface to another. We will describe how the link Floer TQFT can be used to construct lower bounds.