Linking numbers in rational homology 3-spheres, cyclic branched covers and infinite cyclic covers

الأصل · EN

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.