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Multi-virtual knot theory
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DOI：10.1142/S0218216525400024.png)
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Abstract
En 中文
In this paper, we generalize virtual knot theory to multi-virtual knot theory where there are a multiplicity of virtual crossings. Each virtual crossing type can detour over the other virtual crossing types, and over classical or immersed crossings. New invariants of multi-virtual knots and links are introduced and new problems that arise are described. We show how the extensions of the Penrose coloring evaluation for trivalent plane graphs and our generalizations of this to non-planar graphs and arbitrary numbers of colors acts as a motivation for the construction of the multi-virtual theory.
Keywords:
Graph
trivalent graph
cubic graph
perfect matching
Petersen graph
Penrose evaluation, matching polynomial
chromatic polynomial
dichromatic polynomial
Tutte polynomial
formation
coloring
knot diagram
link diagram
virtual knot theory
multi-virtual knot theory
bracket polynomial
chromatic bracket polynomial
parity bracket polynomial
quandle
bi-quandle
generalized quandle
rotational virtuals, multi-virtual link cobordism
multiple welded knot theory
arrow polynomial
multi-virtual braids
multi-virtual Markov theorem
Journal
J
IF:
0.4
Papers:
99
Citations:
0
Organization
Cited Papers
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