Bosonic pentachoron weights and multiplicative 2-cocycles

TL;DR

This paper explores bosonic weights related to four-dimensional Pachner moves, revealing gauge equivalence classes and their parametrization by multiplicative 2-cocycles, with implications for algebraic topological constructions.

Contribution

It introduces a gauge equivalence framework for bosonic pentachoron weights and characterizes their classes using multiplicative 2-cocycles, extending understanding of algebraic realizations of Pachner moves.

Findings

All generic one-boson weights are gauge equivalent.

Two-boson weights' classes are parameterized by multiplicative 2-cocycles.

Generic two-boson weights can be gauge-reduced to delta-function form.

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.