23 citations · 37 across the 8 of their papers we have counts for
10 papers
The virtual flyping theorem
Thomas Kindred
We extend the flyping theorem to alternating links in thickened surfaces and alternating virtual links. The proof of the former result uses work of Boden--Karimi to adapt the autho…
Primeness of alternating virtual links
Thomas Kindred
Using a new tool called lassos, we establish a new correspondence between cellular link {diagrams} on closed surfaces and equivalence classes of virtual link {diagrams}. This is an…
End-essential spanning surfaces for links in thickened surfaces
Thomas Kindred
Let be a cellular alternating link diagram on a closed orientable surface . We prove that if has no removable nugatory crossings then each checkerboard surface from …
Efficient multisections of odd-dimensional tori
Thomas Kindred
Rubinstein--Tillmann generalized the notions of Heegaard splittings of 3-manifolds and trisections of 4-manifolds by defining {\it multisections} of PL -manifolds, which are dec…
A geometric proof of the flyping theorem
Thomas Kindred
In 1898, Tait asserted several properties of alternating knot diagrams. These assertions became known as Tait's conjectures and remained open until the discovery of the Jones polyn…
Crosscap numbers of alternating knots via unknotting splices
Thomas Kindred
Ito-Takimura recently defined a splice-unknotting number for knot diagrams. They proved that this number provides an upper bound for the crosscap number of any prime knot,…
Plumbing is a natural operation in Khovanov homology
Thomas Kindred
Given a connect sum of link diagrams, there is an isomorphism which decomposes unnormalized Khovanov chain groups for the product in terms of normalized chain groups for the factor…
Alternating links have representativity 2
Thomas Kindred
We prove that if is a non-trivial alternating link embedded (without crossings) in a closed surface , then has a compressing disk whose boundary intersects $L…
Heegaard diagrams corresponding to Turaev surfaces
Cody Armond, Nathan Druivenga, Thomas Kindred
We describe a correspondence between Turaev surfaces of link diagrams on and special Heegaard diagrams for adapted to links.
A classification of spanning surfaces for alternating links
Colin Adams, Thomas Kindred
A classification of spanning surfaces for alternating links is provided up to genus, orientability, and a new invariant that we call aggregate slope. That is, given an alternating…