The reduction of quantum invariants of 4-thickenings

Ivelina Bobtcheva, and Frank Quinn. "The reduction of quantum invariants of 4-thickenings." Fundamenta Mathematicae 188.1 (2005): 21-43. <http://eudml.org/doc/283203>.

@article{IvelinaBobtcheva2005,
abstract = {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.},
author = {Ivelina Bobtcheva, Frank Quinn},
journal = {Fundamenta Mathematicae},
keywords = {2-complex; modular invariant},
language = {eng},
number = {1},
pages = {21-43},
title = {The reduction of quantum invariants of 4-thickenings},
url = {http://eudml.org/doc/283203},
volume = {188},
year = {2005},
}

TY - JOUR
AU - Ivelina Bobtcheva
AU - Frank Quinn
TI - The reduction of quantum invariants of 4-thickenings
JO - Fundamenta Mathematicae
PY - 2005
VL - 188
IS - 1
SP - 21
EP - 43
AB - 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.
LA - eng
KW - 2-complex; modular invariant
UR - http://eudml.org/doc/283203
ER -