TBA by Siddhi Krishna
- Series
- Geometry Topology Seminar
- Time
- Monday, April 22, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Siddhi Krishna – Columbia
We'll give a short description of what exactly monopole Floer spectra are, and then explain how to calculate them for AR plumbings, a class of 3-manifolds including Seifert spaces. This is joint work with Irving Dai and Hirofumi Sasahira.
Please Note: Note unusual date and length for the seminar!
It is well known that all contact 3-manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. Hence, an interesting and much studied question asks what properties (e.g. tightness, fillability, vanishing or non-vanishing of various Floer or symplectic homology classes) of contact structures are preserved under various types of contact surgeries. The case for the negative contact surgeries is fairly well understood. The case of positive contact surgeries much more subtle. In this talk, extending an earlier work of the speaker with Conway and Etnyre, I will discuss some new results about symplectic fillability of positive contact surgeries, and in particular we will provide a necessary and sufficient condition for contact (positive) integer surgery along a Legendrian knot to yield a fillable contact manifold. When specialized to knots in the three sphere with its standard tight structure, this result can be rather efficient to find many examples of fillable surgeries along with various obstructions and surprising topological applications. This will report on joint work with T. Mark.
In dimension 4, there exist simply connected manifolds which are homeomorphic but not diffeomorphic; the difference between the distinct smooth structures can be localized using corks. Similarly, there exist diffeomorphisms of simply connected 4-manifolds which are topologically but not smoothly isotopic to the identity. In this talk, I will discuss some preliminary results towards an analogous localization of this phenomena using corks for diffeomorphisms. This project is joint work with Slava Krushkal, Anubhav Mukherjee, and Mark Powell.
For the past 25 years, a key player in contact topology has been the Floer-theoretic invariant called Legendrian contact homology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and is derived from rational symplectic field theory. This includes a Poisson bracket on Legendrian contact homology and a symplectic structure on augmentation varieties. Time permitting, I'll also describe an unexpected connection to cluster theory for a family of Legendrian links associated to positive braids. Parts of this are joint work in progress with Roger Casals, Honghao Gao, Linhui Shen, and Daping Weng.
We prove that the space of circle packings consistent with a given triangulation on a surface of genus at least two is projectively rigid, so that a packing on a complex projective surface is not deformable within that complex projective structure. More broadly, we show that the space of circle packings is a (smooth) submanifold within the space of complex projective structures on that surface.