Abelian link invariants and homology

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3431031· OSTI ID:21362146

Guadagnini, Enore ^[1]; Mancarella, Francesco ^[2]

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1. Dipartimento di Fisica, Universita di Pisa, INFN, Sezione di Pisa, Pisa 56127 (Italy)
2. International School for Advanced Studies, SISSA, Via Beirut 2-4, 34151 Trieste (Italy)

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{sup 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.

• OSTI ID: 21362146
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 6; Other Information: DOI: 10.1063/1.3431031; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
COMPLEMENT
FIELD THEORIES
FUNCTIONS
SPHERES
ORGANIC COMPOUNDS
PROTEINS