대한수학회보 (Bulletin of the Korean Mathematical Society)
- 제35권2호
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- Pages.235-258
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- 1998
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
ALEXANDER POLYNOMIAL FOR LINK CROSSINGS
초록
We define a crossing of a link without referring to a specific projection of the link and describe a construction of a non-normalized Alexander polynomial associated to collections of such crossings of oriented links under an equivalence relation, called homology relation. The polynomial is computed from a special Seifert surface of the link. We prove that the polynomial is well-defined for the homology equivalence classes, investigate its relationship with the combinatorially defined Alexander polynomials and study some of its properties.