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Transactions of the American Mathematical Society

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Homotopy on spatial graphs and the Sato-Levine invariant

Authors: Thomas Fleming and Ryo Nikkuni
Journal: Trans. Amer. Math. Soc. 361 (2009), 1885-1902
MSC (2000): Primary 57M15; Secondary 57M25
Published electronically: November 25, 2008
MathSciNet review: 2465822
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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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Additional Information

Thomas Fleming
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093

Ryo Nikkuni
Affiliation: Institute of Human and Social Sciences, Faculty of Teacher Education, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa, 920-1192, Japan

Keywords: Spatial graph, edge-homotopy, vertex-homotopy, Sato-Levine invariant
Received by editor(s): August 31, 2005
Received by editor(s) in revised form: March 10, 2007
Published electronically: November 25, 2008
Additional Notes: The first author was supported by a Fellowship of the Japan Society for the Promotion of Science for Post-Doctoral Foreign Researchers (Short-Term) (No. PE05003).
The second author was partially supported by a Grant-in-Aid for Scientific Research (B) (2) (No. 15340019), Japan Society for the Promotion of Science.
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