Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3

Autor:	Korepanov, Igor G., Sadykov, Nurlan M.
Rok vydání:	2013
Předmět:	Mathematics - Quantum Algebra Mathematical Physics Mathematics - Algebraic Topology 15A75 57Q99 57R56
Zdroj:	SIGMA 9 (2013), 053, 19 pages
Druh dokumentu:	Working Paper
DOI:	10.3842/SIGMA.2013.053
Popis:	We consider relations in Grassmann algebra corresponding to the four-dimensional Pachner move 3-3, assuming that there is just one Grassmann variable on each 3-face, and a 4-simplex weight is a Grassmann-Gaussian exponent depending on these variables on its five 3-faces. We show that there exists a large family of such relations; the problem is in finding their algebraic-topologically meaningful parameterization. We solve this problem in part, providing two nicely parameterized subfamilies of such relations. For the second of them, we further investigate the nature of some of its parameters: they turn out to correspond to an exotic analogue of middle homologies. In passing, we also provide the 2-4 Pachner move relation for this second case. Comment: this article supersedes arXiv:1301.5581
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1305.3246 Zobrazit plný text záznamu View this record from Arxiv