Homotopy on spatial graphs and generalized Sato-Levine invariants

Details Homotopy on spatial graphs and generalized Sato-Levine invariants Homotopy on spatial graphs and generalized Sato-Levine invariants

2007-10-19

arxiv.org/abs/0710.3627v3

Mathematics

Geometric Topology

16 pages, 13 figures

Scientific paper

Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. Fleming and the author introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the constituent 2-component algebraically split links. In this paper, we construct some new edge (resp. vertex)-homotopy invariants of spatial graphs without any restriction of linking numbers of the constituent 2-component links by applying the generalized Sato-Levine invariant.

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