6 papers
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…
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…
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(Î…