List of Papers

Jun Murakami

  • Generalized Kashaev invariants for knots in three manifolds
  • Volume of a doubly truncated hyperbolic tetrahedron, (with Alexander Kolpakov)
  • Invariants of Handlebody-Knots via Yokota's Invariants (with Atsuhiko Mizusawa)
  • Optimistic limits of the colored Jones polynomials, (with Jinseok Cho)
  • On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume, (with Francesco Costantino)
  • The volume formulas for a spherical tetrahedron
  • The complex volumes of twist knots via colored Jones polynomials, (with Jinseok Cho)
  • Some limits of the colored Alexander invariant of the figure-eight knot and the volume of hyperbolic orbifolds, (with Jinseok Cho)
  • The complex volumes of tiwst knots (with Jinseok Cho and Yoshiuki Yokota)
  • Colored Alexander invariants and cone-manifolds
  • Logarithmic knot invariants arising from restricted quantum groups (with Kiyokazu Nagatomo)
  • Cololored Alexander invariants and cone-manifolds
    • Colored Alexander invariant was first introduced by Akutsu-Deguchi-Ohtsuki, and here a relation with the volume of the cone-manifold is discussed by using the iadea of the volume conjecture.
  • A volume formula for hyperbolic tetrahedra in terms of edge lengths (with Akira Ushijima)
  • On the volume of a hyperbolic and spherical tetrahedron (with Masakazu Yano)
  • Kashaev's conjecture and the Chern-Simons invariants of knots and links (with Hitoshi Murakami, Miyuki Okamoto, Toshie Takata and Yoshiyuki Yokota)
  • Actual computation for the complexified hyperbolic volume conjecture
    • Volume conjecture and its related topics (Japanese) (Kyoto, 2002), Surikaisekikenkyusho Kokyuroku 1279 (2002), 67--85.
  • The colored Jones polynomials and the simplicial volume of a knot (with Hitoshi Murakami)
    • Acta Math. 186 (2001), no. 1, 85--104.
    • Kashaev intoruduced a knot invariant which is conjedtured to relate to the hyperbolic volume of the complement of a hyperbolic knot. In this paper show that Kashaev's invariant is equal to a specialization of the coloered Jones polynomial. This means that the colored Jones polynomial may relate to the hyperolic volume of the complement of a hyperbolic knot. We extend this conjecture to general knots by using the Gromov's simplicial volume.
  • Finite type invariants detecting the mutant knots
    • Knot Thoery -dedicated to Professor Kunio Murasugi for his 70th birthday- Toronto July 13th - 17th, 1999. Editors: M. Sakuma et al., Osaka University, March 2000, pp. 258-267.
    • We show that there is no finite-type invariant of degree
      less than 11 which distinguishes mutant knots.
  • A three-manifold invariant via the Kontsevich integral (with Thang T. Q. Le, Hitoshi Murakami and Tomotada Ohtsuki)
    • Osaka J. Math. 36 (2) (1999), 365-396.
    • In this paper, we show a relation of the Kontsevich invariant concerning to the second Kirby move of links, which is important to construct the universal perturvative invariant.
      We also study the degree 1 part of the universal perturvative invariant concretely and showed that this part coinsides with the Lescop's generalization of the Casson-Walker invariant.
  • On a universal perturbative invariant of 3-manifolds (with Thang T. Q. Le and Tomotada Ohtsuki)
    • Topology 37 (1998), 539-574.
    • In this paper, we constructed the universal perturbative invariant of 3-manifolds from the Kontsevich invariant of links. T. T. Q. Le showed that the universal perturbative invariant is universal for the finite type invariant of rational homology spheres introduced by T. Ohtsuki and S. Garoufaridis. T. Ohtsuki showed that the perturbative SO(3) invariant of rational homology spheres is recovered from the universal perturbative invariant.
  • Topological quantum field theory for the universal quantum invariant (with T. Ohtsuki)
    • Commun. Math. Phys. 188 (1997), 501-520.
    • Errata:
      p. 508 l.7, l.14, l.25,   D_{>n} -> D_{>n(\ell + 1)}
  • Representation of mapping class groups via the universal perturbative invariant
    • Proceedings of Knots 96, ed. S. Suzuki, 1997 World Scientific, pp. 573-586.
    • Errata
  • The Casson invariant for a knot in a 3-manifold
    • Geometry and Physics (Ed. Anderson, Dupont, Pedersen and Swan), Lecture notes in pure and applied mathematics, 184 (1996), 459-469.
  • The universal Vassiliev-Kontsevich invariant for framed oriented links (with Thang T. Q. Le)
    • Compo. Math. 102 (1996), 42-64.
  • Kontsevich's integral for the Kauffman polynomial (with Thang T. Q. Le)
    • Nagoya Math. J. 142 (1996), 39-65.
  • A three-manifold invariant derived from the universal Vassiliev-Kontsevich invariant (with Thang T. Q. Le, Hitoshi Murakami and Tomotada Ohtsuki)
    • Proc. Japan Acad. Ser A. 71 (1995), 125-127.
  • Representations of the category of tangles by Kontsevich's iterated integral (with Thang T. Q. Le)
    • Commun. Math. Phys. 168 (1995), 535-562.
  • Kontsevich's integral for the HOMFLY polynomial and relations between values of multiple zeta functions (with Thang. T. Q. Le)
    • Topology and its appl. 62 (1995), 193-206.
  • Subgraphs of W-graphs and the 3-parallel version polynomial invariants of links (with Mitsuyuki Ochiai)
    • Proc. Japan Acad. Ser A. 70 (1994), 267-270.
    • Erata:
      p. 269, l.9    ... \sigma_1^4 \sigma_2^2 (resp.    
      ----> ... \sigma_1^{-4} \sigma_2^2 (resp.
  • Centralizer algebras of the mixed tensor representations of quantum group $U_q(gl(n, C))$ (with Masashi Kosuda)
    • Osaka J. Math. 30 (1994), 475-507.
  • The Yamada polynomial of spacial graphs and knit algebras
    • Commun. Math. Phys. 155 (1993), 511-522.
  • A state model for the multi-variable Alexander polynomial
    • Pacific J. Math, 157 (1993), 109-135.
    • Errata:
      p.126, l.-4 Let $L_5$ and $L_6$ be four lins ...
      ----> Let $L_5$ and $L_6$ be two lins ...
      p.127, Figure 1
      remove $L_1$, $L_2$, $L_3$, $L_4$, which is not refered in the paper.
  • The centralizer algebras of the mixed tensor representations of quantum group $U_q(gl(n, C))$ and the HOMFLY polynomial of links (with Masashi Kosuda)
    • Proc. Japan Acad. Ser A. 68 (1992), 148-151.
  • Invariants of spatial graphs
    • Advanced Studies in Pure Mathematics 20 (1992), 147-166.
  • On local relations to determine the multi-variable Alexander polynomial of colored links
    • Knot 90 (Osaka, 1990), 455-464, de Gruyter, 1992.
    • Errata:
      p. 457, Figure 5
        L_1 --> L_{-21-2}, L_2 --> L_{1-21},
        L_3 --> L_{2-12}, L_4 --> L_{-12-1}.
      p. 458, Figure 6
        L_5 --> L', L_6 --> L .
  • The free-fermion model in presence of field related to the quantum group $U_q(sl_2)$ of affine type and the multi-variable Alexander polynomial of links
    • Infinite analysis, Advanced Series in Mathmatical Physics, 16 B (1991), 765-772.
  • The representations of the q-analogue of Brauer's centralizer algebras and the Kauffman polynomial of links
    • Publ. Res. Inst. Math. Sci. 26 (1990), 935-945.
  • Solvable lattice models and algebras of face operators
    • Integrable systems in quantum field theory and statistical mechanics, Advanced Studies in Pure Mathematics, 19 (1989), 399-415, Academic Press.
  • The parallel version of polynomial invariants of links (Dr. Thesis)
    • Osaka J. Math. 26 (1989), 1-55.
    • Define parallel versions of the Jones polynomial and its generalizations and study their properties by using representations of the braid groups to some algebras. As a result, it turns out that the 3-parallel version of the HOMFLY polynomial can distinguish two mutant knots (if they are "general").
  • Cyclotomic invariants for links (with Tsuyoshi Kobayashi and Hitoshi Murakami)
    • Proc. Japan Academy, Ser. A. 64 (1988), no,7, 235-238.
  • The Kauffman polynomial of links and representation theory
    • Osaka J. Math. 24 (1987), 745-758.
    • As in the case of Jones polynomial, The Kauffman polynomial of knots and links is expressed by characters of certain series of algebras. Such algebras are also constructed by J. Birman and H. Wenzl in the paper "Braids, link polynomials and a new algebra", Trans. Amer. Math. Soc. 313 (1989), 249-273.

back to my home page
back to Department of Mathematics home page

Jun Murakami
Department of Mathematics
Faculty of Science and Engineering
Waseda University 3-4-1 Ohkubo, Shinjyuku-ku Tokyo 169-8555, JAPAN

mail address