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Akio Kawauchi

2008-10-01
14:00:00 - 15:00:00

Introducing a complexity to spatial graphs

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

We introduce a notion which we call the warping degree for every connected spatial graph (possibly, with vertices of degree one) by defining admissible regular diagrams of the spatial graph. By definition the warping degree takes a value in non-negative integers, by which we can define a notion of a complexity among all the spatial graphs of any given connected graph.
For every connected spatial graph without vertices of degree one, this notion is used to define two kinds of notions of topological invariants. We observe that one of the notions coincides with the unknotting number for a spatial connected plane graph, in particular for a knot.