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arXiv · 1701.07489

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

Igor G. Korepanov
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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.

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Igor G. Korepanov. 2017-03-15. Free fermions on a piecewise linear four-manifold. II: Pachner moves. https://doi.org/10.1007/s00006-017-0811-1

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