2009/10/08 by Nathan Geer, Geer, Nathan, Bertrand Patureau-Mirand +3 · 2 citations
Mathematics · #17B37 #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:17B37 #msc:57M25 #msc:57M27
paper · pdf · doi:10.48550/arxiv.0910.1624
37 pages, 16 figures
arxiv created 2009/11/12 · arxiv updated 2009/12/01
We show that the renormalized quantum invariants of links and graphs in the 3-sphere, derived from tensor categories in ["Modified quantum dimensions and re-normalized link invariants", arXiv:0711.4229] lead to modified 6j-symbols and to new state sum 3-manifold invariants. We give examples of categories such that the associated standard Turaev-Viro 3-manifold invariants vanish but the secondary invariants may be non-zero. The categories in these examples are pivotal categories which are neither ribbon nor semi-simple and have an infinite number of simple objects.