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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homology groups of symmetric quandles and cocycle invariants of links and surface-links


Authors: Seiichi Kamada and Kanako Oshiro
Journal: Trans. Amer. Math. Soc. 362 (2010), 5501-5527
MSC (2010): Primary 57M25, 57Q45; Secondary 55N99, 18G99
Published electronically: May 20, 2010
MathSciNet review: 2657689
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Abstract: We introduce the notion of a quandle with a good involution and its homology groups. Carter et al. defined quandle cocycle invariants for oriented links and oriented surface-links. By use of good involutions, quandle cocyle invariants can be defined for links and surface-links which are not necessarily oriented or orientable. The invariants can be used in order to estimate the minimal triple point numbers of non-orientable surface-links.


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Additional Information

Seiichi Kamada
Affiliation: Department of Mathematics, Hiroshima University, Hiroshima 739-8526, Japan
Email: kamada@math.sci.hiroshima-u.ac.jp

Kanako Oshiro
Affiliation: Department of Mathematics, Hiroshima University, Hiroshima 739-8526, Japan
Email: koshiro@hiroshima-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05131-1
PII: S 0002-9947(2010)05131-1
Keywords: Knot, link, surface-link, knotted surface, quandle, rack, quandle homology, symmetric quandle, good involution.
Received by editor(s): February 18, 2009
Published electronically: May 20, 2010
Additional Notes: The first author’s research was partially supported by Grant-in-Aid for Scientific Research, JSPS
The second author’s research was partially supported by Grant-in-Aid for JSPS Research Fellowships for Young Scientists.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.