9 citations · 43 across the 11 of their papers we have counts for
5 papers · 1 filter
Milnor's Isotopy Invariants and Generalized Link Homotopy
Thomas Fleming, Akira Yasuhara
It has long been known that a Milnor invariant with no repeated index is an invariant of link homotopy. We show that Milnor's invariants with repeated indices are invariants not on…
Intrinsically linked graphs and even linking number
Thomas Fleming, Alexander Diesl
We study intrinsically linked graphs where we require that every embedding of the graph contains not just a non-split link, but a link that satisfies some additional property. Exam…
Virtual Spatial Graphs
Thomas Fleming, Blake Mellor
Two natural generalizations of knot theory are the study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin th…
Homotopy on spatial graphs and the Sato-Levine invariant
Thomas Fleming, Ryo Nikkuni
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy in…
Chord Diagrams and Gauss Codes for Graphs
Thomas Fleming, Blake Mellor
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invar…