
SIGMA 9 (2013), 053, 19 pages arXiv:1305.3246
http://dx.doi.org/10.3842/SIGMA.2013.053
Parameterizing the Simplest GrassmannGaussian Relations for Pachner Move 33
Igor G. Korepanov and Nurlan M. Sadykov
Moscow State University of Instrument Engineering and Computer Sciences, 20 Stromynka Str., Moscow 107996, Russia
Received May 15, 2013, in final form August 08, 2013; Published online August 13, 2013
Abstract
We consider relations in Grassmann algebra corresponding to the fourdimensional Pachner move
33, assuming that there is just one Grassmann variable on each 3face, and a 4simplex weight is
a GrassmannGaussian exponent depending on these variables on its five 3faces.
We show that there exists a large family of such relations; the problem is in finding their
algebraictopologically 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 24 Pachner move relation for this second case.
Key words:
fourdimensional Pachner moves; Grassmann algebras; Clifford algebras; maximal isotropic Euclidean subspaces.
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