Abstract
We characterize the Seifert matrices of periodic knots in S3 up to S-equivalence. Given a periodic knot we construct an equivariant spanning surface F and choose a basis for H1(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 H1(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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
