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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Homotopy on spatial graphs and the Sato-Levine invariant
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by Thomas Fleming and Ryo Nikkuni PDF
Trans. Amer. Math. Soc. 361 (2009), 1885-1902 Request permission

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
  • Email: tfleming@math.ucsd.edu
  • Ryo Nikkuni
  • Affiliation: Institute of Human and Social Sciences, Faculty of Teacher Education, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa, 920-1192, Japan
  • MR Author ID: 662147
  • Email: nick@ed.kanazawa-u.ac.jp
  • 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.
  • © Copyright 2008 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 1885-1902
  • MSC (2000): Primary 57M15; Secondary 57M25
  • DOI: https://doi.org/10.1090/S0002-9947-08-04510-8
  • MathSciNet review: 2465822