Free fermions on a piecewise linear four-manifold. II: Pachner moves

Abstract

This is the second in a series of papers where we construct an invariant of a four-dimensional piecewise linear manifold $M$ with a given middle cohomology class $h\in H^2(M,\mathbb{C})$. This invariant is the square root of the torsion of unusual chain complex introduced in Part I (arXiv:1605.06498) of our work, multiplied by a correcting factor. Here we find this factor by studying the behavior of our construction under all four-dimensional Pachner moves, and show that it can be represented in a multiplicative form: a product of same-type multipliers over all 2-faces, multiplied by a product of same-type multipliers over all pentachora.

20 pages. v2: two of three Experimental Results now proven, and many small improvements

References in corpus (5)

• Two-cocycles give a full nonlinear parameterization of the simplest 3--3 relation
• Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves
• Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3
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• Free fermions on a piecewise linear four-manifold. I: Exotic chain complex

Cited by in corpus (3)

• Nonconstant hexagon relations and their cohomology
• Bosonic pentachoron weights and multiplicative 2-cocycles
• Free fermions on a piecewise linear four-manifold. I: Exotic chain complex