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Homotopy on spatial graphs and the Sato-Levine invariant

Thomas Fleming·Ryo Nikkuni
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Abstract

Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the 2-component constituent algebraically split links and show examples of non-splittable spatial graphs up to edge (resp. vertex)-homotopy, all of whose constituent links are link-homotopically trivial.

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BibTeXRIS

Thomas Fleming, Ryo Nikkuni. 2005-09-01. Homotopy on spatial graphs and the Sato-Levine invariant. https://doi.org/10.1090/s0002-9947-08-04510-8

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