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- Title
The Markov theorems for spatial graphs and handlebody-knots with Y-orientations.
- Authors
Ishii, Atsushi
- Abstract
We establish the Markov theorems for spatial graphs and handlebody-knots. We introduce an IH-labeled spatial trivalent graph and develop a theory on it, since both a spatial graph and a handlebody-knot can be realized as the IH-equivalence classes of IH-labeled spatial trivalent graphs. We show that any two orientations of a graph without sources and sinks are related by finite sequence of local orientation changes preserving the condition that the graph has no sources and no sinks. This leads us to define two kinds of orientations for IH-labeled spatial trivalent graphs, which fit a closed braid, and is used for the proof of the Markov theorem. We give an enhanced Alexander theorem for orientated tangles, which is also used for the proof.
- Subjects
MARKOV processes; GRAPH theory; HANDLEBODIES; MATHEMATICAL equivalence; TANGLES (Knot theory); MATHEMATICAL sequences
- Publication
International Journal of Mathematics, 2015, Vol 26, Issue 14, p-1
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X15501165