A+ CATEGORY SCIENTIFIC UNIT

Virtual knot theory—unsolved problems

Volume 188 / 2005

Roger Fenn, Louis H. Kauffman, Vassily O. Manturov Fundamenta Mathematicae 188 (2005), 293-323 MSC: Primary 57M25. DOI: 10.4064/fm188-0-13

Abstract

The present paper gives a quick survey of virtual and classical knot theory and presents a list of unsolved problems about virtual knots and links. These are all problems in low-dimensional topology with a special emphasis on virtual knots. In particular, we touch new approaches to knot invariants such as biquandles and Khovanov homology theory. Connections to other geometrical and combinatorial aspects are also discussed.

Authors

  • Roger FennDepartment of Mathematics
    University of Sussex
    Sussex BN1 9RF, England
    e-mail
  • Louis H. KauffmanDepartment of Mathematics
    Statistics and Computer Science
    University of Illinois at Chicago
    851 South Morgan St.
    Chicago, IL 60607-7045, U.S.A.
    e-mail
  • Vassily O. ManturovDepartment of Mechanics and Mathematics
    Moscow State University
    119992, GSP-2, Leninskie Gory, MSU, Moscow, Russia
    e-mail

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