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Mayberry-Murasugi's formula for links in homology 3-spheres
Author(s):
Joan
Porti
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3423-3431.
MSC (2000):
Primary 57M12, 57Q10;
Secondary 57M25, 20K01
Posted:
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:
-
- [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:
10.1090/S0002-9939-04-07458-1
PII:
S 0002-9939(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
Posted:
May 20, 2004
Additional Notes:
This work was partially supported by DGICYT through grant BFM2000-0007
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2004,
American Mathematical Society
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