8 papers
U torsion structure in Heegaard Floer homology
Yuhui Chen, Shunyu Wan
We construct infinite families of Brieskorn spheres with three singular fibers for which the difference between the largest and the second largest length of -torsion in their He…
Heegaard Floer knot trace invariants, exotic 4-manifolds, and symplectic obstructions
Jennifer Hom, Shunyu Wan
We show that the numerical invariants and coming from knot Floer homology are knot -trace invariants for any integer , resolving the remaining case in Hay…
The next-to-top term of the knot Floer homology of some non-fibered knots
Fraser Binns, Shunyu Wan
Sivek conjectured that the rank of knot Floer homology in the next-to-top Alexander grading is at least the rank in the top Alexander grading. Baldwin and Vela-Vick verified this c…
Exotic 's, RBG Links, and End Floer Homology
Sean Eli, Shunyu Wan
We give the first pair of non-diffeomorphic exotic 's made by attaching diffeomorphic Casson handles onto diffeomorphic disk complements. Our examples are obtained us…
Surgeries on knots and tight contact structures
Zhenkun Li, Shunyu Wan, Hugo Zhou
For any knot in and any positive rational , we show that smooth -surgery on always admits a tight contact structure. More specifically, the tightness is dete…
On Legendrian representatives of non-fibered knots
Zhenkun Li, Shunyu Wan
We show that in if is a non-trivial knot that realizes the three-dimensional Thurston-Bennequin bound (i.e. has a Legendrian representative with $tb(Λ)-…
Negative contact surgery on Legendrian non-simple knots
Shunyu Wan, Hugo Zhou
We prove that for any pair of Legendrian representatives of the Chekanov-Eliashberg twist knots with different LOSS invariants, any negative rational contact -surgery with $r\ne…
Tight contact structures on some families of small Seifert fiber spaces
Shunyu Wan
Suppose is a knot in a 3-manifold , and that admits a pair of distinct contact structures. Assume that has Legendrian representatives in each of these contact struct…