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# $B;d$NO@J8(B

$B=PHG$5$l$?O@J8!"%W%l%W%j%s%H!"Js9p=8!J(Breferee$B$D$-!K$N869F$r(B $B;d$,8&5f3hF0$r$7$?=gHV$K$J$i$Y$^$7$?!#(B 1. Ideal points and incompressible surfaces in two-bridge knot complements, J. Math. Soc. Japan, 46, (1994) 51-87. (p,q) two bridge knot group $B!J(Bknot $B$NJd6u4V$N4pK\72!K$N(B
SL_2(C) $BI=8=!J(BSL_2(C) $B$X$N=F17?!K$N(B character variety $B!JI=8=A4BN$N$D$/$k6u4V$r6&Lr$G$o$C$?$b$N!K$N(B
$B$9$Y$F$N(B ideal point $B!JL58B1sE@!"3F(B (p,q) $B$K$D$$FM-8B8D7+J$$!K$r(B
p/q $B$NO"J,?tE83+$rMQ$$F40A4K%j%9%H%"%C%W7?!#(B B B=N7W;;,99KDl!"9YFN(B ideal point B,A4KFr8=9Nr(B B^N"?jK7?;dO!"3F(B knot BKD$$$F(B ideal point $B$,8=$l$kH~$7$$(B B%a%+%K%:%!J0lHLO@!K,"kG"m&!"H$$$&3N?.$r$b$D$K$$?C?!#(B B!J7+7!"8=>uGO!"=N0lHLO@,INh&JbNG"kN+!"(B BLCNG"k!#!K(B 2. (with H. Murakami and M. Okada) Invariants of three-manifolds derived from linking matrices of framed links, Osaka J. Math, 29, (1992) 545-572. BNL;R(B U(1) BITJQNLrAH_9go;E*K9=@.7!"=NCMO(B M BN%3%[%b%m%8!<4DrMQ$$$F5-=R$G$-$k$3$H$r<($7$?!#(B $B$"$H$K$J$C$F!"(BH. Murakami and M. Okada $B$,FHN)$KDj5A$7$?(B $BITJQNL$HF1CM$G$"$k$3$H$,$o$+$j!"6&Cx$K$J$k!#(B 3. (with Y. Akutsu and T. Deguchi) Invariants of colored links, J. Knot Theory and Its Rami., 1, (1992) 161-184. $BNL;R72(B U_q(sl_2) $B$O(B q $B$,#1$N$Y$-:,$N$H$-!"DL>o$H$3$H$J$k(B $BI=8=$NB2$r$b$D$,!"$=$l$rMxMQ$7$F(B link $B$NITJQNL$r9=@.$7$?!#(B 4. (with T. Deguchi) Invariants of colored links and a property of the Clebsch-Gordan coefficients of$U_q(\frak g)$, Proceedings of the 21st International Conference on Differential Geometric Methods in Theoretical Physics, edited by C.N. Yang, M.L. Ge and X.W. Zhou, World Scientific (1993), 263--266. $B;d$O$3$N2q5D$K=P@J$b$7$F$$J$$$N$KL>A0$r$D$i$M$k$3$H$K$J$C$?!#(B
$B?=$7Lu$J$$3HG"k!#(B 5. Colored ribbon Hopf algebras and universal invariants of framed links, J. Knot Theory and Its Rami., 2, (1993) 211-232. 3. BNITJQNL!JB?9<0!Kr3HD%7F!"(Balgebra U_q(sl_2) B<+?HKCMrbD(B BITJQNLr9=@.7?!#(B3. BGMQ$$$?I=8=$N;XI8$GCM$r$H$k$H!"(B
3. $B$NITJQNL$,2sI|$9$k$N$G$"$k!#$A$J$_$K!"(BU_q(sl_2) $B$NI=8=$r(B
$BMQ$$FDj5A5lk9YFN(B knot invariant B!J?H(P(B Jones BB?9<0(B BJI!K,=NJ}K!G2sI|9k!#=3G(B universal invariant BH$$$&L>A0$r$D$1$?!#(B

6. Invariants of 3-manifolds derived from universal invariants of framed links,
Math. Proc. Camb. Phil. Soc., 117, (1995) 259-273.
$B#3o$N9=@.K!$rI|=,$9$k$H!"(B
$B;XI8$N$&$^$$@~7A7k9gG(B universal invariant BNCMrHkH(B B#3 BH3m,!";XI8N@~7A7k9gG+1J$$$h$&$J@~7A $B#3
7. A polynomial invariant of integral homology 3-spheres,
Math. Proc. Camb. Phil. Soc., 117, (1995) 83-112.
$BNL;R(B SO(3) $BITJQNL(B \tau_r $B$r(B q-1 $B$GE83+$7$?$H$-$N(B n $B $B$"$k0UL#$G(B r $B$K$h$i$J$$3Hr<(7?!#=N78?trD+$$(B formal power series $B$KCM$r$b$DITJQNL$,Dj5A$G$-$k!#(B
$BEv=i!";d$O$3$N(B formal power series $B$OE,Ev$JJQ?tJQ49$N$b$H$G(B polynomial $B$K$J$k$G$"$m$&!"$H$$&4E$$4|BT$r$b$C$F$$??a!"(B B%?%%H%k,3&JCF7^C?N@,!" formal power series B,<}B+7F@5B'4X?tKJk+I&+O(B B4JC1KOo+iJ$$!"$H8e$GH=L@$9$k!#(B

8. Invariants of links and 3-manifolds related to a quantum group,
Thesis, Univ. of Tokyo, (1993)
$B3X0LO@J8$N7A$K$9$k$?$a(B 3. $B$H(B 5. $B$H(B 6. $B$r9gBN$5$;$FJT=8$7$?$b$N!#(B

9. How to construct ideal points of SL_2(C) representation spaces
of knot groups,
Topology Appl. 93 (1999) 131-159.
$B0lHL$K(B knot group $B$N(B ideal point $B!J(B1. $B$N%3%a%s%H;2>H!K$r(B
$B6qBNE*$K9=@.$9$kJ}K!$r$"$?$($?!#(B 10. (with R. Riley) Representations of 2-bridge knot groups on 2-bridge knot groups, unfinished draft. Riley $B;a$H$N88$N6&Cx$G$"$k!#6&F18&5f$,F\:B$7$?$N$O!"(B $B;d$,EE;R%a!<%k$K$h$k6&F18&5f$N:nK!$r$o$-$^$($J$+$C$?$+$i(B
$B$G$"$m$&!#$3$N<:GT$G;d$,$($?6571$O!"$?$H$(Aj $B$J$m$&$H$b!"$P$+CzG+$JJ8BN$r$/$:$5$J$$!"H$$$&$3$H$G$"$k!#(B $B$=$&$7$J$$H!"%a!<%krRsQsKdjHj7F$$$k$?$a!"(B $B$"$C$H$$&^K!"Jl"CF7^&!#(B B8&5fFbMFN@bL@hjb!V<+J,,IsJKK;7$$$+!W$H$$&3H(B BN@bL@NJ},D9/JCF-?i!"*7^$$$G$"$k!#(B

11. A polynomial invariant of rational homology 3-spheres,
Invent. Math. 123 (1996), 241-257
$BO@J8$r$+$/$?$a$K$O!J$=$NJ,Ln$N8&5f$r%j!<%I$G$-$k$h$&$J!K(B
$BE/3X$,8l$l$J$1$l$P$J$i$J$$!"H$$$&$3$H$r $B$3$NO@J8$G$=$N$h$&$JE/3X$,$+$?$l$F$$ko1GOJ/!"(B B=lO:#8eN2]BjG"k!#(B 12. Finite type invariants of integral homology 3-spheres, J. Knot Theory and its Rami. 5 (1996), 101-115 Vassiliev invariant B!J(Bknot BNITJQNL!KN#3 B33m_G"k!##3 B,"k+iKO!"=&$$$&$b$N$,$"$k$K$A$,$$J$$!"(B $B$H$*$b$C$?$N$G$"$k!#M-8B7?$NDj5A$K(B algebraically split $B$H$$&?M9)E*H*b(k>r7orD+C??a!"Ev;~O3NO@J8N(B BFbMFKITK~G"C?,!"3N8&5fO#2G/8eK?7?J?JE8r(B B_;O8ak!#(B 13. (with S. Yamada) Quantum SU(3) invariants via linear skein theory, J. Knot Theory and its Rami. 6 (1997) 373--404. Lickorish BKhk(B linear skein theory BrMQ$$$?(B
$BNL;R(B SU(2) $BITJQNL$N9=@.$r$_$J$i$C$F!"(B $BF1$8J}?K$K$h$jNL;R(B SU(3) $BITJQNL$r9=@.$9$k!#(B
$B$H$b$+$/!"3($rJQ7A$9$k$@$1$G#3 $BITJQ@-$N>ZL@$,$G$-$F$7$^$&$?$a!"(B
linear skein theory $B$O=i?4 $B$?$@$7!"(BLie $B4D$N%F%s%=%kI=8=$NJ,2r$N$7$+$?$J$I(B $BGX7J$r$7$C$F$$lP!"8zN(h/7W;;r99ak3H,(B BG-k!J8zN(,$$$$!"H$$$&$N$O0U30$K=EMW$G$"$k!K$N$G!"(B $B2?$b$7$i$J$/$F$b$h$$!"H$$$&$o$1$G$O$J$$!#(B 14. (with H. Murakami, S. Yamada) HOMFLY polynomial via an invariant of colored planar graphs, l'Enseignement mathematique {\bf 44} (1998) 325--360. 13. BN SU(n) linear skein theory BH$$$&$b$N$,$^$@$J$$!#(B B=3G(B planar graph BNITJQNLrD+CFI,MWJ9YFNbNr(B B9=@.7F7^&!#4pK\E*JJdBjN>ZL@O!"N>JUr=l>l(B B9=@.7F_;FEy7$$$3$H$r$_$k!"$H$$C?D4;RGJ5l!"(B linear skein theory BH$$$&4QE@!J4X78<0$G$7$P$C$F$$/!K(B B+iO B:G=iK4pK\@_Djr7?8eO!">ZL@O3(rJQ7A9k@1G9YF(B B3H?jk!"H$$$&$N$,L%NO$G$"$k!#(B 15. (with H. Murakami) Quantum$Sp(n)$invariant of links via an invariant of colored planar graphs, Kobe J. Math. 13, (1996) 191--202. 14. $B$G$3$j$:$K$5$i$K(B Sp(n) $B$X$H$9$9$!#(B
$B$7$+$7!"(BLie $B4D$O(B A $B7?$,H~$7$$!"H$$$&$N$r
16. (with T.Q.T Le, H. Murakami, J. Murakami)
A three-manifold invariant derived from the universal Vassiliev-Kontsevich invariant,
Proc. Japan Acad., 171, (1995) 125--127.
17. $B$NM=9p$G$"$k!#(B 17. (with T. Le, H. Murakami and J. Murakami) A three-manifold invariant via the Kontsevich integral, Osaka J. Math. 36 (2), (1999), 365--396. link $B$N$9$Y$F$NNL;RITJQNL$OIaJWNL;RITJQNL!J(BKontsevich integral$B!K(B $B$K$h$C$FE}0l$5$l$F$7$^$C$?!##3 link $B$NNL;RITJQNL$N#1 $B$=$NIaJWNL;RITJQNL$+$i#3 $B$H$*$b$&$N$O<+A3$NM_5a$G$"$k!#K\O@J8$G$O!"(B
$B%[%b%m%8!<72$N0L?t$H(B Casson $BITJQNL$,Cj=P$G$-$?!#(B

18. (with S. Garoufalidis)
On finite type invariant of 3-manifolds III: manifold weight systems,
Topology 37 (1998) 227--243.
12. $B$GDj5A$7$?M-8B7?ITJQNL$N6u4V$G(B AS and IHX relations $B$,(B
$B$J$j$?$D$3$H$r<($9!#$3$N8&5f$K(B AS and IHX relations $B$,(B
$BD>@\8=$l$?$N$O!"$&$l$7$$8m;;G"C?!#(B BEv=i!";dO!"(B12. BGDj5A7?M-8B7?ITJQNLN6u4VO(B B!J(Balgebraically split BH$$$&!"$9$8$,$o$k$=$&$J>r7o$N$?$a$K!K(B $B$=$s$J$K$-$l$$GOJ$$!"$H;W$$9~sG$$$?$N$G$"$k!#(B

19. On some invariants of 3-manifolds,
in "Geometry and Physics",
the Proceedings on Geometry and Physics, Aarhus 1995,
edited by J.E. Andersen, J. Dupont, H. Pedersen, and A. Swann,
lecture notes in pure and applied mathematics 184,
Marcel Dekker, inc., New York (1997) 411-427.
$B%*!<%U%9Bg3X$O2wE,$G$"$C$?!#$+$NCO$G$O(B
$B!V$@$^$C$F$$FOL5;k5lk!WH$$$&2$JF?M$N$7$-$?$j$r3X$V!#(B

20. (with H. Murakami)
Quantum $Sp(2)$ invariants of three-manifolds at eighth and tenth roots of unity,
in ditto, 429-443.
$B#8>h:,$H#1#0>h:,$N$_$N7k2L$,$^$H$a$i$l$F$$k!#(B BNL;R(B Sp(2) BITJQNLGO!"(Blinear skein theory B,7ilF$$$k$N$@$,!"(B
$B2f!9$O0lHL$N(B roots of unity $B$G$N(B magic element $B$N9=@.$,(B $B$G$-$J$+$C$?$N$G$"$k!#$3$NO@J8$N7k2L<+BN$O%*%j%8%J%k$J$N$@$,!"(B
$BJs9p=8$K$@$9$3$H$K$J$C$?!#(B

21. (with S. Garoufalidis)
On finite type 3-manifold invariants V: rational homology 3-spheres,
in ditto, 445-457.
$B;d$O$3$N7k2L$K$OITK~$G$"$k!#M-M}%[%b%m%8!<5eLL$X$N(B $BM-8B7?ITJQNL$N3HD%$K$D$$FO!"$$$D$+40A47hCe$7$?$H$*$b$&!#(B 22. (with T. Le and J. Murakami) An invariant of 3-manifolds derived from the universal Vassiliev-Kontsevich invariant, preprint, 1995. 23. $B$NM=9p!#(B 23. (with T. Le and J. Murakami) On a universal perturbative quantum invariant of 3-manifolds, Topology 37 (1998) 539-574. $B$3$NO@J8$G!"(B17. $B$G$NL\I8$rC#@.$7$?!#(B $B$9$J$o$A!"(Bchord diagram $B$N6u4V$r(B AS and IHX relations $B$N$_$G(B $B$o$C$?6u4V$KCM$r$b$D#3 $BIaJWNL;RITJQNL$+$i9=@.$9$k!#$3$NITJQNL$r#3 $BIaJWNL;RITJQNL$H$h$V$3$H$K$7$?!#(B

24. Combinatorial quantum method in 3-dimensional topology,
MSJ Memoirs 3, Math. Soc. Japan, 1999.
$B$=$NF|K\8lLu(B $B!VNL;RITJQNL$r$a$0$k(B3$B $B=EE@NN0h8&5f(B231$BL58B2D@QJ,7O!"%l%/%A%c!<%N!<%H(B 15 25. (with J. Murakami) Topological Quantum Field Theory for the universal quantum invariant Commun. Math. Phys. 188 (1997) 501-520. 26. The perturbative$SO(3)$invariant of rational homology 3-spheres recovers from the universal perturbative invariant. Topology 39 (2000) 1103--1135. 27. The perturbative$SO(3)$invariant of homology circles, Proceedings of the Conference on Low Dimensional Topology, edited by H. Nencka, Contemporary Math. 233, Amer. Math. Soc., (1999) 141--151. 28. A filtration of the set of integral homology 3-spheres Proceedings of ICM, Berlin, 1998, Documenta Math. Extra Volume ICM 1998 II, invited lectures, 473--482. 29. (with H. Murakami) Finite type invariants of knots via their Seifert matrices, Asian J. Math. 5 (2001) 379--386. 30. Quantum invariants, --- A study of knots, 3-manifolds, and their sets, Series on Knots and Everything, 29. World Scientific Publishing Co., Inc., 2002. 31. A cabling formula for the 2-loop polynomial of knots, Publ. Res. Inst. Math. Sci. 40 (2004) 949--971. 32. On the 2-loop polynomial of knots, Geometry & Topology 11 (2007) 1357--1475. 33. Equivariant quantum invariants of the infinite cyclic covers of knot complements, Intelligence of Low Dimensional Topology 2006, Series on Knots and Everything 40, World Scientific Publishing Co., Inc., (2007) 253--262. 34. (with D. Moskovich) Vanishing of 3-loop Jacobi diagrams of odd degree, J. Combin. Theory Ser. A. 114 (2007) 919--930. 35. (with R. Riley and M. Sakuma) Epimorphisms between 2-bridge link groups, Geometry & Topology Monographs 14 (2008) 417--450. 36. Invariants of knots derived from equivariant linking matrices of their surgery presentations, Internat. J. Math. 20 (2009) 883--913. 37. Perturbative invariants of 3-manifolds with the first Betti number 1, Geometry & Topology 14 (2010) 1993--2045. 38. (with T. T. Q. Le and T. Kuriya) The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant, J. Topology 5 (2012) 458--484. 39. A refinement of the LMO invariant for 3-manifolds with the first Betti number 1, in preparation. 40. On the asymptotic expansion of the Kashaev invariant of the 5_2 knot, Quantum Topology 7 (2016) 669--735. 41. (with T. Takata) On the Kashaev invariant and the twisted Reidemeister torsion of two-bridge knots, Geometry & Topology 19 (2015) 853--952. 42. (with Y. Yokota) On the asymptotic expansions of the Kashaev invariant of the knots with 6 crossings, Math. Proc. Camb. Phil. Soc. (to appear). 43. On the asymptotic expansion of the quantum SU(2) invariant at$q = exp(4 \pi \sqrt{-1}/N)$for closed hyperbolic 3-manifolds obtained by integral surgery along the figure-eight knot, Algebraic & Geometric Topology 18 (2018) 4187--4274. 44. On the asymptotic expansion of the Kashaev invariant of the hyperbolic knots with seven crossings, Internat. J. Math. 28 (2017), no. 13, 1750096, 143 pp. 45. (with T. Takata) On the quantum SU(2) invariant at$q=\exp(4\pi\sqrt{-1}/N)\$ and the twisted Reidemeister torsion for some closed 3-manifolds,
Commun. Math. Phys. 370 (2019) 151--204.