Abelian link invariants and homology

Details Abelian link invariants and homology Abelian link invariants and homology

2010-04-29

arxiv.org/abs/1004.5211v1

J. Math. Phys. 51, 062301 (2010)

Physics

Mathematical Physics

18 pages, 3 figures; to be published in Journal of Mathematical Physics

Scientific paper

10.1063/1.3431031

We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link -in a generic manifold M- is homologically trivial, the associated observables coincide with the observables of the sphere S^3. Finally we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.

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