Donaldson's theorem, Heegaard Floer homology, and knots with unknotting number one

Autor:	Joshua Evan Greene
Rok vydání:	2014
Předmět:	Combinatorics Floer homology General Mathematics Donaldson's theorem Unknotting number Mathematics::Algebraic Topology Mathematics::Symplectic Geometry Mathematics::Geometric Topology Alternating knot Mathematics
Zdroj:	Advances in Mathematics. 255:672-705
ISSN:	0001-8708
Popis:	We establish an obstruction to unknotting an alternating knot by a single crossing change. The obstruction is lattice-theoretic in nature, and combines Donaldson's diagonalization theorem with an obstruction developed by Ozsvath and Szabo using Heegaard Floer homology. As an application, we enumerate the alternating 3-braid knots with unknotting number one, and show that each has an unknotting crossing in its standard alternating diagram.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b9fe2cbb1f6a3a3cfea73eeb5b426e7a https://doi.org/10.1016/j.aim.2014.01.018 Zobrazit plný text záznamu Full Text from ScienceDirect