Mathematics – Geometric Topology
Scientific paper
2010-09-07
Journal of Knot Theory and Its Ramifications Vol. 18, No. 6 (2009) 729-755
Mathematics
Geometric Topology
23 pages, a version of a published paper with minor corrections
Scientific paper
Homology of the circle with non-trivial local coefficients is trivial. From this well-known fact we deduce geometric corollaries concerning links of codimension two. In particular, the Murasugi-Tristram signatures are extended to invariants of links formed of arbitrary oriented closed codimension two submanifolds of an odd-dimensional sphere. The novelty is that the submanifolds are not assumed to be disjoint, but are transversal to each other, and the signatures are parametrized by points of the whole torus. Murasugi-Tristram inequalities and their generalizations are also extended to this setup.
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