6 papers · 1 filter
Deciding strong quasipositivity and quasipositivity
Marc Kegel, Qiuyu Ren
We present two results concerning the decidability of (strong) quasipositivity of links in the 3-sphere. First, using a result of Dynnikov--Prasolov, we provide an algorithm to dec…
Trisection invariants of 4-manifolds are uncomputable
Nathan M. Dunfield, Marc Kegel, Shana Yunsheng Li +1
We prove that two invariants of smooth 4-manifolds defined in terms of trisections are uncomputable: the trisection genus and the Kirby-Thompson L-invariant. That is, there does no…
Multisections and bridge positions in arbitrary dimensions
Sylvain Courte, Delphine Moussard, Qiuyu Ren +1
Multisections were defined by Ben Aribi--Courte--Golla--Moussard as a way to decompose closed manifolds into -handlebodies, which is a generalization of Heegaard splittings and…
Insensitivity of Khovanov homology under rim surgery
Qiuyu Ren, Fang-Rong Zhan
We show that rim surgery on a smooth, oriented, properly embedded surface in does not change the map on Khovanov homology induced by the surface, answering a question raised…
Families of cosmetic surgeries
Qiuyu Ren
We construct infinite families of chirally cosmetic surgeries on chiral hyperbolic knots and purely cosmetic surgeries on hyperbolic manifolds with multiple cusps, disproving conje…
Ribbon concordance of fibered knots and compressions of surface homeomorphisms
Ian Agol, Qiuyu Ren
We prove that simplicial volume and dilatation are monotone under ribbon concordance between fibered knots in , and that every fibered knot has only finitely many predecessors…