This article is cited in 6 papers

Research Papers

Spatial graphs, tangles and plane trees

V. M. Nezhinskij<sup>ab

a</sup> St. Petersburg State University, Mathematics and Mechanics Faculty
^b Herzen State Pedagogical University of Russia, St. Petersburg

Abstract: All (finite connected) spatial graphs are supplied with an additional structure – the replenished skeleton and its disk framing, – in such a way that the problem of isotopic classification of spatial graphs endowed with this structure admits reduction to two problems: the (classical) problem of isotopic classification of tangles and the (close to classical) problem of isotopic classification of plane trees equipped with an additional structure, specifically, a set of hanging vertices and a fixed vertex (the root of the tree) in this set.

Keywords: chord diagram, tangle, plane tree, spacial graph, spacial tortoise, smooth isotopy.

MSC: 51B10

Received: 21.11.2016

 English version: St. Petersburg Mathematical Journal, 2020, 31:6, 1055–1063

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