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. (C) 2010 American Institute of Physics. [doi:10.1063/1.3431031]
Abelian link invariants and homology
GUADAGNINI, ENORE;
2010-01-01
Abstract
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. (C) 2010 American Institute of Physics. [doi:10.1063/1.3431031]I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
