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Free fermions on a piecewise linear four-manifold. II: Pachner moves
- Source :
- Adv. Appl. Clifford Algebras (2017) 27:3129-3147
- Publication Year :
- 2017
-
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.<br />Comment: 20 pages. v2: two of three Experimental Results now proven, and many small improvements
Details
- Database :
- arXiv
- Journal :
- Adv. Appl. Clifford Algebras (2017) 27:3129-3147
- Publication Type :
- Report
- Accession number :
- edsarx.1701.07489
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00006-017-0811-1