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Functorial maps and weak parities

Published 2 Nov 2012 in math.GT | (1211.0403v1)

Abstract: Functorial maps and weak parities are equivalent descriptions of rules of substitution virtual crossings for classical in diagrams of a knot in a way compatible with Reidemeister moves. We introduce the notion of maximal weak parity and describe it for knots in a given closed oriented surface. This weak parity defines a projection from virtual knots to classical knots.

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