Bosonic pentachoron weights and multiplicative 2-cocycles

Abstract

Gaussian pentachoron weights can be used for constructing algebraic realizations of four-dimensional Pachner moves. Here, we consider a natural `gauge equivalence' for such weights with one and two bosonic - i.e., commuting - variables on 3-faces. For the one-boson case, all generic weights turn out to be gauge equivalent. For the two-boson case, and generic weights, their gauge equivalence classes are parameterized by multiplicative 2-cocycles. Moreover, a generic two-boson weight can be reduced by a gauge transformation to a delta-function form.

26 pages. v2: a proof of a Pachner 3--3 relation added

References in corpus (3)

• Two-cocycles give a full nonlinear parameterization of the simplest 3--3 relation
• Hexagon cohomologies and polynomial TQFT actions
• Free fermions on a piecewise linear four-manifold. II: Pachner moves

Cited by in corpus (2)

• Hexagon cohomologies and polynomial TQFT actions
• Heptagon relations parameterized by simplicial 3-cocycles