Two-cocycles give a full nonlinear parameterization of the simplest 3--3 relation

Abstract

A parameterization of Grassmann-algebraic relations corresponding to the Pachner move 3--3 is proposed. In these relations, each 4-simplex is assigned a Grassmann weight depending on five anticommuting variables associated with its 3-faces. The weights are chosen to have the "simplest" form - a Grassmann--Gaussian exponent or its analogue (satisfying a similar system of differential equations). Our parameterization works for a Zariski open set of such relations, looks relevant from the algebraic-topological viewpoint, and reveals intriguing nonlinear relations between objects associated with simplices of different dimensions.

25 pages. v3: the accepted version. The final publication is available at link.springer.com, see journal-ref and DOI here

References in corpus (2)

• Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3
• Special 2-cocycles and 3--3 Pachner move relations in Grassmann algebra

Cited by in corpus (8)

• Simplex and Polygon Equations
• Nonconstant hexagon relations and their cohomology
• Multiplicative expression for the coefficient in fermionic 3-3 relation
• Odd-gon relations and their cohomology
• Free fermions on a piecewise linear four-manifold. II: Pachner moves
• Bosonic pentachoron weights and multiplicative 2-cocycles
• Free fermions on a piecewise linear four-manifold. I: Exotic chain complex
• The photography method: solving pentagon equation