Abstract
Virtual links are generalizations of classical links that can be represented by links embedded in a "thickened" surface Σ×I, product of a Riemann surface of genus h with an interval. In this paper, we show that virtual alternating links and tangles are naturally associated with the 1/N2 expansion of an integral over N×N complex matrices. We suggest that it is sufficient to count the equivalence classes of these diagrams modulo ordinary (planar) flypes. To test this hypothesis, we use an algorithm coding the corresponding Feynman diagrams by means of permutations that generates virtual diagrams up to 6 crossings and computes various invariants. Under this hypothesis, we use known results on matrix integrals to get the generating functions of virtual alternating tangles of genus 1 to 5 up to order 10 (i.e. 10 real crossings). The asymptotic behavior for n large of the numbers of links and tangles of genus h and with n crossings is also computed for h=1,2,3 and conjectured for general h.
Sign-in/Register to access full text options 
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.
