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LINKING NUMBERS IN RATIONAL HOMOLOGY 3-SPHERES, CYCLIC BRANCHED COVERS AND INFINITE CYCLIC COVERS (2001)
| Citations: | 3 - 1 self |
BibTeX
@MISC{Przytycki01linkingnumbers,
author = {Józef H. Przytycki},
title = {LINKING NUMBERS IN RATIONAL HOMOLOGY 3-SPHERES, CYCLIC BRANCHED COVERS AND INFINITE CYCLIC COVERS},
year = {2001}
}
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Abstract
We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in Q and in Q(Z[t,t −1]) respectively, where Q(Z[t,t −1]) denotes the quotient field of Z[t,t −1]. It is known that the modulo-Z linking number in the rational homology 3-sphere is determined by the linking matrix of the framed link and that the modulo-Z[t,t −1] linking number in the infinite cyclic cover of the complement of a knot is determined by the Seifert matrix of the knot. We eliminate ‘modulo Z ’ and ‘modulo Z[t,t −1]’. When the finite cyclic cover of the 3-sphere branched over a knot is a rational homology 3-sphere, the linking number of a pair in the preimage of a link in the 3-sphere is determined by the Goeritz/Seifert matrix of the knot.
