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Mayberry-Murasugi's formula for links in homology 3-spheres


Author: Joan Porti
Journal: Proc. Amer. Math. Soc. 132 (2004), 3423-3431
MSC (2000): Primary 57M12, 57Q10; Secondary 57M25, 20K01
DOI: https://doi.org/10.1090/S0002-9939-04-07458-1
Published electronically: May 20, 2004
MathSciNet review: 2073320
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Abstract: We prove the Mayberry-Murasugi formula for links in homology 3-spheres, which was proved before only for links in the 3-sphere. Our proof uses Franz-Reidemeister torsions.


References [Enhancements On Off] (What's this?)

  • [Fo] R. H. Fox. Free differential calculus. III. Subgroups. Ann. of Math. (2) 64 (1956), 407-419. MR 20:2374
  • [Fr] W. Franz. Torsionsideale, Torsionsklassen und Torsion. J. Reine Angew. Math. 176 (1936), 113-124.
  • [HS] J. Hillman and M. Sakuma. On the homology of finite abelian coverings of links. Canad. Math. Bull. 40 (1997), no. 3, 309-315. MR 98i:57010
  • [MM] J. P. Mayberry and K. Murasugi. Torsion-groups of abelian coverings of links. Trans. Amer. Math. Soc. 271 (1982), no. 1, 143-173. MR 84d:57004
  • [M1] J. Milnor. Two complexes which are homeomorphic but combinatorially distinct. Ann. of Math. (2) 74 (1961), 575-590. MR 24:A2961
  • [M2] J. Milnor, A duality theorem for Reidemeister torsion. Ann. of Math. (2) 76 (1962), 137-147. MR 25:4526
  • [M3] J. Milnor, Whitehead torsion. Bull. Amer. Math. Soc. 72 (1966), 358-426. MR 33:4922
  • [Sa] M. Sakuma. Homology of abelian coverings of links and spatial graphs. Canad. J. Math. 47 (1995). MR 96d:57008
  • [Se] J.-P. Serre. Représentations linéaires des groupes finis. Hermann, Paris, 1967. MR 38:1190
  • [T] V. G. Turaev. Reidemeister torsion in knot theory. Russian Math. Surveys 41 (1986), no. 1, 119-182. MR 87i:57009

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Additional Information

Joan Porti
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
Email: porti@mat.uab.es

DOI: https://doi.org/10.1090/S0002-9939-04-07458-1
Keywords: Branched coverings, Franz-Reidemeister torsion
Received by editor(s): June 14, 2003
Received by editor(s) in revised form: July 1, 2003
Published electronically: May 20, 2004
Additional Notes: This work was partially supported by DGICYT through grant BFM2000-0007
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2004 American Mathematical Society

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