The reduction of quantum invariants of 4-thickenings

• Autorzy: Ivelina Bobtcheva , Frank Quinn
• Języki publikacji: EN

Abstrakty

EN

We study the sensibility of an invariant of 2-dimensional CW complexes in the case when it comes as a reduction (through a change of ring) of a modular invariant of 4-dimensional thickenings of such complexes: it is shown that if the Euler characteristic of the 2-complex is greater than or equal to 1, its invariant depends only on homology. To see what is happening when the Euler characteristic is smaller than 1, we use ideas of Kerler and construct, from any tortile category, an invariant of 4-thickenings which, if the category is modular, is a normalization of the Reshetikhin-Turaev invariant, and if the category is symmetric, depends only on the spine and the second Whitney number of the thickening. Then we show that the so(3) quantum invariant at a 5th root of unity has its reduction, and this reduction is able to distinguish complexes with the same homology groups when the Euler characteristic is smaller than 1.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57M20: Two-dimensional complexes
• 57R56: Topological quantum field theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 188
• Numer: 1
• Strony: 21-43

Daty

wydano

2005

Twórcy

autor

Ivelina Bobtcheva

• Dipartimento di Scienze Matematiche, Università di Ancona, Via Brecce Bianche 1, 60131 Ancona, Italy

autor

Frank Quinn

• Department of Mathematics, Virginia Polytechnic Institute, and State University, Blacksburg, VA 24060, U.S.A.

Identyfikatory

DOI

10.4064/fm188-0-2