Seifert matrices of periodic knots

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We characterize the Seifert matrices of periodic knots in S-3 up to S-equivalence. Given a periodic knot we construct an equivariant spanning surface F and choose a basis for H-1(F) in such a way that the Seifert matrix has a special form exhibiting the periodicity. Conversely, given such a Seifert matrix we construct a periodic knot that realizes it. We exhibit the decomposition of H-1(F; C) into eigenspaces of the periodic action, orthogonal to each other with respect to the Seifert pairing. Consequently we obtain Murasugi's formula for the Alexander polynomial of the periodic knot.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2007-01
Language
English
Article Type
Article
Keywords

POLYNOMIALS

Citation

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.16, no.1, pp.45 - 57

ISSN
0218-2165
DOI
10.1142/S021821650700518X
URI
http://hdl.handle.net/10203/87048
Appears in Collection
MA-Journal Papers(저널논문)
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