For a compact orientable 3-manifold M, the Thurston norm on H2 (M, ÖM; Z)= H'(M; Z)
measures the minimal topological complexity of a surface representing a particular …

The Kakimizu complex $ MS (K) $ for a knot $ K\subset\mathbb {S}^ 3$ is the simplicial
complex with vertices the isotopy classes of minimal genus Seifert surfaces in the exterior of …

Seifert surfaces for genus one hyperbolic knots in the 3–sphere Page 1 msp Algebraic &
Geometric Topology 19 (2019) 2151–2231 Seifert surfaces for genus one hyperbolic knots in the …

A knot k in S3 has tunnel number one, if there exist an arc τ embedded in S3, with k∩ τ=∂ τ,
such that S 3− int N (k∪ τ) is a genus 2 handlebody. In this paper we construct for each …

NON-SIMPLE LINKS WITH TUNNEL NUMBER ONE A link l is non-simple if there is an essential
annulus or torus properly embedded in th Page 1 PROCEEDINGS OF THE AMERICAN …

For a compact orientable 3-manifold M, the Thurston norm on H2 (M,∂ M; Z)∼= H 1 (M; Z)
measures the minimal topological complexity of a surface representing a particular …

In this paper we construct an infinite family of hyperbolic knots, each having a Dehn surgery
which produces a manifold containing an incompressible torus, which hits the core of the …

We show that the only knots that are tunnel number one and genus one are those that are
already known: $2 $-bridge knots obtained by plumbing together two unknotted annuli and …

Let M be a simple 3-manifold, ie one that contains no essential sphere, disk, annulus or
torus, with a torus boundary component∂ 0M. One is interested in obtaining upper bounds …

Let M be S3, S1× S2, or a lens space L (p, q), and let k be a (1, 1)-knot in M. We show that if
there is a closed meridionally incompressible surface in the complement of k, then the …