4 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…
Small undecidable groups and unrecognizable 4-manifolds
Marc Kegel, Shana Yunsheng Li, Qiuyu Ren
We construct a -generator -relator group with unsolvable word problem. We use the group to construct two fixed-size Adian--Rabin families of group presentations, one with …
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…
The search for exotic knot traces
Marc Kegel, Jonathan Spreer
Two distinct knots are said to be friends if their complements, filled along the 0-slope, produce diffeomorphic 3-manifolds. In this article, we develop a practical algorithm, impl…