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

Porti, Joan

doi:10.1090/S0002-9939-04-07458-1

Mayberry-Murasugi’s formula for links in homology 3-spheres
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Proc. Amer. Math. Soc. 132 (2004), 3423-3431 Request permission

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

Ralph H. Fox, Free differential calculus. III. Subgroups, Ann. of Math. (2) 64 (1956), 407–419. MR 95876, DOI 10.2307/1969592
W. Franz. Torsionsideale, Torsionsklassen und Torsion. J. Reine Angew. Math. 176 (1936), 113–124.
J. A. Hillman and M. Sakuma, On the homology of finite abelian coverings of links, Canad. Math. Bull. 40 (1997), no. 3, 309–315. MR 1464839, DOI 10.4153/CMB-1997-037-9
John P. Mayberry and Kunio Murasugi, Torsion-groups of abelian coverings of links, Trans. Amer. Math. Soc. 271 (1982), no. 1, 143–173. MR 648083, DOI 10.1090/S0002-9947-1982-0648083-1
John Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math. (2) 74 (1961), 575–590. MR 133127, DOI 10.2307/1970299
John Milnor, A duality theorem for Reidemeister torsion, Ann. of Math. (2) 76 (1962), 137–147. MR 141115, DOI 10.2307/1970268
J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358–426. MR 196736, DOI 10.1090/S0002-9904-1966-11484-2
Makoto Sakuma, Homology of abelian coverings of links and spatial graphs, Canad. J. Math. 47 (1995), no. 1, 201–224. MR 1319696, DOI 10.4153/CJM-1995-010-2
Jean-Pierre Serre, Représentations linéaires des groupes finis, Hermann, Paris, 1967 (French). MR 0232867
V. G. Turaev, Reidemeister torsion in knot theory, Uspekhi Mat. Nauk 41 (1986), no. 1(247), 97–147, 240 (Russian). MR 832411