Zobrazeno 1 - 10
of 174
pro vyhledávání: '"Hom, Jennifer"'
We introduce an oriented rational band move, a generalization of an ordinary oriented band move, and show that if a knot $K$ in the three-sphere can be made into the $(n+1)$-component unlink by $n$ oriented rational band moves, then $K$ is rationally
Externí odkaz:
http://arxiv.org/abs/2311.11507
A knot in $S^3$ is topologically slice if it bounds a locally flat disk in $B^4$. A knot in $S^3$ is rationally slice if it bounds a smooth disk in a rational homology ball. We prove that the smooth concordance group of topologically and rationally s
Externí odkaz:
http://arxiv.org/abs/2304.06265
We consider manifold-knot pairs $(Y,K)$ where $Y$ is a homology sphere that bounds a homology ball. We show that the minimum genus of a PL surface $\Sigma$ in a homology ball $X$ such that $\partial (X, \Sigma) = (Y, K)$ can be arbitrarily large. Equ
Externí odkaz:
http://arxiv.org/abs/2301.04729
We prove that there are homology three-spheres that bound definite four-manifolds, but any such bounding four-manifold must be built out of many handles. The argument uses the homology cobordism invariant $\Gamma$ from instanton Floer homology.
Externí odkaz:
http://arxiv.org/abs/2210.06607
The unknotting number of knots is a difficult quantity to compute, and even its behavior under basic satelliting operations is not understood. We establish a lower bound on the unknotting number of cable knots and iterated cable knots purely in terms
Externí odkaz:
http://arxiv.org/abs/2206.04196
We prove an involutive analog of the dual knot surgery formula of Eftekhary and Hedden-Levine. We also compute a small model for the local equivalence class of the involutive dual knot complex.
Comment: 47 pages, 7 figures. Comments welcomed!
Comment: 47 pages, 7 figures. Comments welcomed!
Externí odkaz:
http://arxiv.org/abs/2205.12798
We prove first-order naturality of involutive Heegaard Floer homology, and furthermore construct well-defined maps on involutive Heegaard Floer homology associated to cobordisms between three-manifolds. We also prove analogous naturality and functori
Externí odkaz:
http://arxiv.org/abs/2201.12906
We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite number of $\mathbb{Z}$-valued, linearly independent homology concordance h
Externí odkaz:
http://arxiv.org/abs/2110.14803
Autor:
Hom, Jennifer
We review some recent results in knot concordance and homology cobordism. The proofs rely on various forms of Heegaard Floer homology. We also discuss related open problems.
Comment: 23 pages, 1 figure
Comment: 23 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2108.10400
Autor:
Hom, Jennifer
A knot is said to be slice if it bounds a smooth disk in the 4-ball. For 50 years, it was unknown whether a certain 11 crossing knot, called the Conway knot, was slice or not, and until recently, this was the only one of the thousands of knots with f
Externí odkaz:
http://arxiv.org/abs/2107.09171