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arXiv · 1605.06498

Free fermions on a piecewise linear four-manifold. I: Exotic chain complex

Igor G. Korepanov
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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 $\mathbb C$-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.

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Igor G. Korepanov. 2016-11-29. Free fermions on a piecewise linear four-manifold. I: Exotic chain complex. https://doi.org/10.1007/s00006-016-0746-y

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