Heegaard splittings of knot exteriors
Y Moriah - Workshop on Heegaard Splittings, 2007 - msp.org
The goal of this survey paper is to sum up known results about Heegaard splittings of knot
exteriors in S 3 and present them with some historical perspective. Until the mid 80's …
exteriors in S 3 and present them with some historical perspective. Until the mid 80's …
Rank and genus of 3-manifolds
T Li - Journal of the American Mathematical Society, 2013 - ams.org
We construct a counterexample to the Rank versus Genus Conjecture, ie a closed orientable
hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus …
hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus …
[PDF][PDF] Primitive spatial graphs and graph minors
M Ozawa, Y Tsutsumi - Rev. Mat. Complut, 2007 - mat.ucm.es
ABSTRACT Robertson, Seymour, and Thomas characterized linkless embeddings of graphs
by flat embeddings, and determined the obstruction set for linkless embeddings. In this …
by flat embeddings, and determined the obstruction set for linkless embeddings. In this …
Unknotting annuli and handlebody-knot symmetry
YS Wang - Topology and its Applications, 2022 - Elsevier
By Thurston's hyperbolization theorem, irreducible handlebody-knots are classified into
three classes: hyperbolic, toroidal, and atoroidal cylindrical. It is known that a non-trivial …
three classes: hyperbolic, toroidal, and atoroidal cylindrical. It is known that a non-trivial …
The tree of knot tunnels
S Cho, D McCullough - Geometry & Topology, 2009 - msp.org
We present a new theory which describes the collection of all tunnels of tunnel number 1
knots in S 3 (up to orientation-preserving equivalence in the sense of Heegaard splittings) …
knots in S 3 (up to orientation-preserving equivalence in the sense of Heegaard splittings) …
Uniqueness of bridge surfaces for 2-bridge knots
M Scharlemann, M Tomova - Mathematical Proceedings of the …, 2008 - cambridge.org
Uniqueness of bridge surfaces for 2-bridge knots Page 1 Math. Proc. Camb. Phil. Soc. (2008),
144, 639 c 2008 Cambridge Philosophical Society doi:10.1017/S0305004107000977 …
144, 639 c 2008 Cambridge Philosophical Society doi:10.1017/S0305004107000977 …
Levelling an unknotting tunnel
H Goda, M Scharlemann, A Thompson - Geometry & Topology, 2000 - msp.org
It is a consequence of theorems of Gordon-Reid [J. Knot Theory Ram. 4 (1995) 389–409]
and Thompson [Topology 36 (1997) 505–507] that a tunnel number one knot, if put in thin …
and Thompson [Topology 36 (1997) 505–507] that a tunnel number one knot, if put in thin …
Computing Heegaard genus is NP-hard
Abstract We show that Heegaard Genus≤ g, the problem of deciding whether a triangulated
3-manifold admits a Heegaard splitting of genus less than or equal to g, is NP-hard. The …
3-manifold admits a Heegaard splitting of genus less than or equal to g, is NP-hard. The …
Alternating links on surfaces and volume bounds
E Kalfagianni, JS Purcell - arXiv preprint arXiv:2004.10909, 2020 - arxiv.org
Weakly generalised alternating knots are knots with an alternating projection onto a closed
surface in a compact irreducible 3-manifold, and they share many hyperbolic geometric …
surface in a compact irreducible 3-manifold, and they share many hyperbolic geometric …
Classification of alternating knots with tunnel number one
M Lackenby - arXiv preprint math/0103217, 2001 - arxiv.org
arXiv:math/0103217v2 [math.GT] 5 Aug 2002 Page 1 arXiv:math/0103217v2 [math.GT] 5 Aug
2002 CLASSIFICATION OF ALTERNATING KNOTS WITH TUNNEL NUMBER ONE MARC …
2002 CLASSIFICATION OF ALTERNATING KNOTS WITH TUNNEL NUMBER ONE MARC …