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Journal of Topology Advance Access originally published online on April 1, 2008
Journal of Topology 2008 1(2):285-305; doi:10.1112/jtopol/jtn002
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© 2008 London Mathematical Society

Cobordism of knots on surfaces

Vladimir Turaev

IRMA, Université Louis Pasteur–CNRS, 7 Rue René Descartes, F-67084 Strasbourg, France
Department of Mathematics, Indiana University, Rawles Hall, 831 East 3rd St, Bloomington, IN 47405, USA vtouraev@indiana.edu

We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.

Received May 14, 2007.

2000 Mathematics Subject Classification 57M27



References

  1. Asaeda M., Przytycki J., Sikora A. ‘Categorification of the Kauffman bracket skein module of I-bundles over surfaces’. Algebr. Geom. Topol. (2004) 4:1177–1210.[CrossRef]
  2. Carter J. S. ‘Closed curves that never extend to proper maps of disks’. Proc. Amer. Math. Soc. (1991) 113:879–888.[CrossRef]
  3. Carter J. S., Kamada S., Saito M. ‘Stable equivalence of knots on surfaces and virtual knot cobordisms’. J. Knot Theory Ramifications (2002) 11:311–322.[CrossRef]
  4. Cimasoni D., Turaev V. ‘A generalization of several classical invariants of links’. Osaka J. Math. (2007) 44:531–561.
  5. Cotta-Ramusino P., Rinaldi M. ‘On the algebraic structure of link-diagrams on a 2-dimensional surface’. Comm. Math. Phys. (1991) 138:137–173.[CrossRef]
  6. Fenn R., Turaev V. ‘Weyl algebras and knots’. J. Geom. Phys. (2007) 57:1313–1324.[CrossRef]
  7. Fiedler T. Gauss diagram invariants for knots and links (2001) Dordrecht: Kluwer Academic Publishers. Mathematics and its Applications 532.
  8. Kamada S. Braid and knot theory in dimension four (2002) Providence, RI: American Mathematical Society. Mathematical Surveys and Monographs 95.
  9. Kauffman L. ‘Virtual knots theory’. European J. Combin. (1999) 20:663–690.[CrossRef]
  10. Kauffman L., Manturov V. ‘Virtual knots and links’. Tr. Mat. Inst. Steklova (2006) 252. Geom. Topol. Diskret. Geom. i Teor. Mnozh. 114–133 (Russian); Proc. Steklov Inst. Math. 252 (2006), 104–121 (English).
  11. Kuperberg G. ‘What is a virtual link’. Algebr. Geom. Topol. (2003) 3:587–591.[CrossRef]
  12. Livingston C. ‘A survey of classical knot concordance’. Handbook of knot theory (2005) Amsterdam: Elsevier. 319–347.
  13. Turaev V. ‘Skein quantization of Poisson algebras of loops on surfaces’. Ann. Sci. École Norm. Sup. (1991) 24(4):635–704.
  14. Turaev V. ‘Virtual strings’. Ann. Inst. Fourier (Grenoble) (2004) 54:2455–2525.

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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
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Right arrow Articles by Turaev, V.
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Add to CiteULike   Add to Connotea   Add to Del.icio.us  
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