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math.GT2011★ 3 cited
Cosmetic crossings and Seifert matrices
Cheryl Balm, Stefan Friedl, Efstratia Kalfagianni +1
We study cosmetic crossings in knots of genus one and obtain obstructions to such crossings in terms of knot invariants determined by Seifert matrices. In particular, we prove that…
math.GT2011
Cosmetic crossings of genus one knots
Cheryl Balm, Efstratia Kalfagianni
We show that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application…