Kazuo Habiro

Research Institute for Mathematical Sciences
Kyoto University

Publications and preprints

  1. (with A. Beliakova, A.D. Lauda and B. Webster) Cyclicity for categorified quantum groups , J. Algebra 452 (2016) 118-132
  2. (with T.Q.T. Le) Unified quantum invariants for integral homology spheres associated with simple Lie algebras , preprint arXiv:1503.03549, to appear in Geometry and Topology
  3. (with A. Beliakova, A.D. Lauda and B. Webster) Current algebras and categorified quantum groups , preprint arXiv:1412.1417
  4. (with A. Beliakova, Z. Guliyev and A.D. Lauda) Trace as an alternative decategofication functor , Acta Math. Vietnam. 39 (2014) 425-480
  5. (with A. Beliakova, A.D. Lauda and M. Živković) Trace decategorification of categorified quantum sl(2) , Math. Ann. (published on line)
  6. (with T. Widmer) Kirby calculus for null-homologous framed links in 3-manifolds , preprint arXiv:1404.0282, J. Topol. (accepted)
  7. (with A. Beliakova) A categorification of the ribbon element in quantum sl(2), preprint arXiv:1304.7585
  8. (with E. Contreras) Borromean surgery equivalence of spin 3-manifolds with boundary, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 14 (2015) 1271-1282
  9. (with T. Widmer) On Kirby calculus for null-homotopic framed links in 3-manifolds, Algebr. Geom. Topol. 14 (2014) 115-134
  10. (with G. Massuyeau) From mapping class groups to monoids of homology cobordisms: a survey, Handbook of Teichmüller Theory III, 465-529, IRMA Lect. Math. Theor. Phys., 17, European Mathematical Society, 2012.
  11. (with G. Massuyeau) Symplectic Jacobi diagrams and the Lie algebra of homology cylinders, J. Topology 2 (2009) 527-569
  12. (with D. Cheptea and G. Massuyeau) A functorial LMO invariant for Lagrangian cobordisms, Geom. Topol. 12 (2008) 1091-1170
  13. A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres, Invent. Math. 171 (2008) 1-81
  14. (with J.-B. Meilhan) On the Kontsevich integral of Brunnian links, Algebr. Geom. Topol. 6 (2006) 1399-1412
  15. (with J.-B. Meilhan) Finite type invariants and Milnor invariants for Brunnian links, Internat. J. Math. 19 (2008) 747-766
  16. Brunnian links, claspers and Goussarov-Vassiliev finite type invariants, Math. Proc. Camb. Phil. Soc. 142 (2007), 459-468.
  17. Replacing a graph clasper by tree claspers, preprint, October 2005.
  18. Refined Kirby calculus for integral homology spheres, Geom. Topol. 10 (2006) 1285-1317
  19. Bottom tangles and universal invariants, Algebr. Geom. Topol. 6 (2006) 1113-1214
  20. An integral form of the quantized enveloping algebra of sl2 and its completions, J. Pure Appl. Alg. 211 (2007), 265-292
  21. Cyclotomic completions of polynomial rings, Publ. Res. Inst. Math. Sci. 40 (2004), 1127-1146.
  22. On the quantum sl2 invariants of knots and integral homology spheres. In: Invariants of knots and 3-manifolds (Kyoto 2001), Geometry and Topology Monographs, Vol. 4 (2002), 55-68.
  23. (with S. Kamada, Y. Matsumoto and K. Yoshikawa) Algebraic formulae for the q-inverse in a free group, J. Math. Sci. Univ. Tokyo 8 (2001), 721-734.
  24. (with A. Shima) Finite type invariants of ribbon 2-knots, II, Topology Appl. 111 (2001), no.3, 265-287.
  25. (with Y. Marumoto and Y. Yamada) Gluck surgery and framed links in 4-manifolds. In: Knots in Hellas '98 (Delphi, 1998), 80-93, Ser. Knots Everything, 24, World Sci. Publishing, River Edge, NJ, (2000).
  26. On the colored Jones polynomials of some simple links. In: Recent progress towards the volume conjecture (Kyoto, 2000). RIMS Kokyuroku, No. 1172, (2000), 34-43.
  27. Claspers and finite type invariants of links, Geom. Topol. 4 (2000), 1-83.
  28. (with T. Kanenobu and A. Shima) Finite type invariants of ribbon 2-knots. In: Low-dimensional topology (Funchal, 1998), 187-196, Contemp. Math., 233, Amer. Math. Soc., Providence, RI, (1999).
  29. Claspers and Vassiliev skein modules, Ph. D. thesis, University of Tokyo, 1997.



3次元多様体のWitten-Reshetikhin-Turaev不変量について , 2003年度日本数学会年会トポロジー分科会講演アブストラクト, 2003年3月.

A functor on the category of bottom tangles in homology handlebodies, 研究集会「多様体のトポロジーの未来へ」(2004年11月)予稿.

Local moves in tangle categories, 研究集会「結び目のトポロジー」(2004年12月)報告集原稿.

Clasp-pass-moves on knots, draft, 1993.

Intelligence of Low-dimensional Topology (June 2-4, 2010, RIMS)