Free fermions on a piecewise linear four-manifold. I: Exotic chain complex
arXiv:1605.06498 · doi:10.1007/s00006-016-0746-y
Abstract
Recently, an algebraic realization of the four-dimensional Pachner move 3--3 was found in terms of Grassmann--Gaussian exponentials, and a remarkable nonlinear parameterization for it, going in terms of a -valued 2-cocycle. Here we define, for a given triangulated four-dimensional manifold and a 2-cocycle on it, an `exotic' chain complex intimately related to the mentioned parameterization, thus providing a basis for algebraic realizations of all four-dimensional Pachner moves.
23 pages. v2: new and better `gauge' for operators proposed, and many small improvements