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Fibred Knots of Genus 2 Formed by Plumbing Hopf Bands
Author(s) -
Melvin P. M.,
Morton H. R.
Publication year - 1986
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-34.1.159
Subject(s) - fibered knot , genus , mathematics , pure mathematics , biology , zoology
Fibred knots of genus 2 have Conway polynomial 1+ c 1 z 2 ± z 4 . We show that the polynomials 1+4 kz 2 + z 4 and 1+(4 k +2) z 2 − z 4 cannot arise for a knot formed by plumbing Hopf bands. Further properties of the monodromy mod 2 in the case where c 1 is even shows that none of Burde's genus 2 fibred knots with c 1 , even are formed by plumbing Hopf bands.