@article{ASENS_2002_4_35_2_153_0, author = {McMullen, Curtis T.}, title = {The {Alexander} polynomial of a $3$-manifold and the {Thurston} norm on cohomology}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {153--171}, publisher = {Elsevier}, volume = {Ser. 4, 35}, number = {2}, year = {2002}, doi = {10.1016/s0012-9593(02)01086-8}, mrnumber = {1914929}, zbl = {1009.57021}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/s0012-9593(02)01086-8/} }
TY - JOUR AU - McMullen, Curtis T. TI - The Alexander polynomial of a $3$-manifold and the Thurston norm on cohomology JO - Annales scientifiques de l'École Normale Supérieure PY - 2002 SP - 153 EP - 171 VL - 35 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/s0012-9593(02)01086-8/ DO - 10.1016/s0012-9593(02)01086-8 LA - en ID - ASENS_2002_4_35_2_153_0 ER -
%0 Journal Article %A McMullen, Curtis T. %T The Alexander polynomial of a $3$-manifold and the Thurston norm on cohomology %J Annales scientifiques de l'École Normale Supérieure %D 2002 %P 153-171 %V 35 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/s0012-9593(02)01086-8/ %R 10.1016/s0012-9593(02)01086-8 %G en %F ASENS_2002_4_35_2_153_0
McMullen, Curtis T. The Alexander polynomial of a $3$-manifold and the Thurston norm on cohomology. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 35 (2002) no. 2, pp. 153-171. doi : 10.1016/s0012-9593(02)01086-8. http://archive.numdam.org/articles/10.1016/s0012-9593(02)01086-8/
[1] Hyperbolic invariants of knots and links, Trans. Amer. Math. Soc. 326 (1991) 1-56. | MR | Zbl
, , ,[2] Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928) 275-306. | JFM | MR
,[3] Intersection theory of manifolds with operators with applications to knot theory, Ann. of Math. 65 (1957) 340-356. | MR | Zbl
,[4] Knots, Walter de Gruyter, 1985. | MR | Zbl
, ,[5] Genus of alternating link types, Ann. of Math. 69 (1959) 258-275. | MR | Zbl
,[6] Introduction to Knot Theory, Springer-Verlag, 1977. | MR | Zbl
, ,[7] Dunfield N., Alexander and Thurston norms of fibered 3-manifolds, Pacific J. Math., To appear. | MR | Zbl
[8] Knots, links and 4-manifolds, Invent. Math. 134 (1998) 363-400. | MR | Zbl
, ,[9] Free differential calculus I, II, III, Ann. of Math. 57, 59, 64 (1956) 547-560, 196-210, 407-419. | MR | Zbl
,[10] Fibrations over S1 with pseudo-Anosov monodromy, in: Travaux de Thurston sur les surfaces, Astérisque, 66-67, 1979, pp. 251-265. | Numdam | Zbl
,[11] Foliations and genera of links, Topology 23 (1984) 381-394. | MR | Zbl
,[12] Detecting fibred links in S3, Comment. Math. Helv. 61 (1986) 519-555. | MR | Zbl
,[13] Some aspects of classical knot theory, in: Knot Theory (Proc. Sem., Plans-sur-Bex, 1977), Lecture Notes in Math., 685, Springer-Verlag, 1978. | MR | Zbl
,[14] Algebraic Topology, Benjamin/Cummings Publishing, 1981. | MR | Zbl
, ,[15] How to construct all fibered knots and links, Topology 21 (1972) 263-280. | MR | Zbl
,[16] Alexander Ideals of Links, Lecture Notes in Math., 895, Springer-Verlag, 1981. | MR | Zbl
,[17] Torsion points on an algebraic subset of an affine torus, Internat. Math. Res. Notices (1996) 953-982. | MR | Zbl
,[18] Alexander stratifications of character varieties, Ann. Inst. Fourier (Grenoble) 47 (1997) 555-583. | Numdam | MR | Zbl
,[19] Lectures on 3-Manifold Topology, American Mathematical Society, 1980. | MR
,[20] Embedded surfaces and gauge theory in three and four dimensions, in: Surveys in Differential Geometry, Vol. III (Cambridge, MA, 1996), Int. Press, 1998, pp. 243-298. | MR | Zbl
,[21] Scalar curvature and the Thurston norm, Math. Res. Lett. 4 (1997) 931-937. | MR | Zbl
, ,[22] Polynomial invariants for fibered 3-manifolds and Teichmüller geodesics for foliations, Ann. Scient. Éc. Norm. Sup. 33 (2000) 519-560. | Numdam | MR | Zbl
,[23] 4-manifolds with inequivalent symplectic forms and 3-manifolds with inequivalent fibrations, Math. Res. Lett. 6 (1999) 681-696. | MR | Zbl
, ,[24] =Milnor torsion, Math. Res. Lett. 3 (1996) 661-674. | MR | Zbl
, ,[25] Infinite cyclic coverings, in: Collected Papers, Vol. 2. The Fundamental Group, Publish or Perish, 1994, pp. 71-89. | Zbl
,[26] On the genus of the alternating knot, I, II, J. Math. Soc. Japan 10 (1958) 94-105, 235-248. | MR | Zbl
,[27] On a certain subgroup of the group of an alternating link, Amer. J. Math. 85 (1963) 544-550. | MR | Zbl
,[28] Homology branched surfaces: Thurston's norm on H2(M3), in: (Ed.), Low-dimensional Topology and Kleinian Groups, Cambridge Univ. Press, 1986, pp. 253-272. | MR | Zbl
,[29] Knots and Links, Publish or Perish, 1976. | MR | Zbl
,[30] Constructions of fibred knots and links, in: Algebraic and Geometric Topology, Proc. Sympos. Pure Math., 32, American Mathematical Society, 1978, pp. 55-60. | MR | Zbl
,[31] A norm for the homology of 3-manifolds, Mem. Amer. Math. Soc. 339 (1986) 99-130. | MR | Zbl
,[32] The Alexander polynomial of a three-dimensional manifold, Math. USSR Sb. 26 (1975) 313-329. | MR | Zbl
,[33] Vidussi S., The Alexander norm is smaller than the Thurston norm: a Seiberg-Witten proof, Preprint 99-6, École Polytechnique.
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