44 citations · 165 across the 21 of their papers we have counts for
11 papers · 1 filter
The quasi-isomorphism class of the Kakimizu complex
Jessica E. Banks
It has been shown that the Kakimizu complex of a knot is quasi-isomorphic to for some . We give a lower bound on , matching the upper bound previously g…
Genus and fibredness of certain three-bridge links
Jessica E. Banks
For each three-bridge link of a certain form, we construct a taut Seifert surface for the link and establish whether the link is fibred. Using this, we also give the genus and fibr…
The Birman exact sequence for 3-manifolds
Jessica E. Banks
We study the Birman exact sequence for compact --manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold and the mapping clas…
Monodromy action on unknotting tunnels in fiber surfaces
Jessica E. Banks, Matt Rathbun
In "Tunnel one, fibered links", the second author showed that the tunnel of a tunnel number one, fibered link can be isotoped to lie as a properly embedded arc in the fiber surface…
Point-pushing in 3-manifolds
Jessica E. Banks
We study the Birman exact sequence for compact 3-manifolds.
Knots with many minimal genus Seifert surfaces
Jessica E. Banks
Roberts proved that a family of alternating, arborescent, prime knots each have at least distinct minimal genus Seifert surfaces, where is the genus of the knot in q…
The Kakimizu complex of a split link
Jessica E. Banks
We study the Kakimizu complex of a split link. As part of this, we also study Seifert surfaces and the Kakimizu complex for a non-split link in a 3-ball. In addition, we show that…
The Kakimizu complex of a connected sum of links
Jessica E. Banks
We show that $|MS(L_1 # L_2)|=|MS(L_1)|\times|MS(L_2)|\times\mathbb{R}$ when and are any non-split and non-fibred links. Here denotes the Kakimizu complex of a…
Minimal genus Seifert surfaces for alternating links
Jessica E. Banks
We give a complete proof of results announced by Hirasawa and Sakuma describing explicitly the Kakimizu complex of a non-split, prime, special, alternating link.
Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial
Jessica E. Banks
We give a geometric proof of the following result of Juhasz. \emph{Let be the leading coefficient of the Alexander polynomial of an alternating knot . If then $K…
On links with locally infinite {K}akimizu complexes
Jessica E. Banks
We show that the Kakimizu complex of a knot may be locally infinite, answering a question of Przytycki--Schultens. We then prove that if a link only has connected Seifert surfa…