Korepanov, I. G. Free fermions on a piecewise linear four-manifold. I: Exotic chain complex. (English) Zbl 1391.15081 Adv. Appl. Clifford Algebr. 27, No. 2, 1411-1430 (2017). This work focuses on algebraic realizations of four-dimensional Pachner moves. The paper provides a basis for constructing realizations of all such moves. The key component are Grassmann-Gaussian exponentials of quadratic forms of anticommuting variables. Reviewer: Martin Plešinger (Liberec) Cited in 1 ReviewCited in 2 Documents MSC: 15A66 Clifford algebras, spinors 15A63 Quadratic and bilinear forms, inner products 81T99 Quantum field theory; related classical field theories Keywords:piecewise linear manifold; four-manifold; topological quantum field theory Software:CLIFFORD PDFBibTeX XMLCite \textit{I. G. Korepanov}, Adv. Appl. Clifford Algebr. 27, No. 2, 1411--1430 (2017; Zbl 1391.15081) Full Text: DOI arXiv References: [1] Abłamowicz, R., Lounesto, P.: On Clifford Algebras of a Bilinear Form with an Antisymmetric Part. In: Abłamowicz, R., Lounesto, P., Parra, J.M. (eds.) Clifford Algebras with Numeric and Symbolic Computations. Birkhäuser, Boston (1996) · Zbl 0856.15028 [2] Berezin, F.A.: The Method of Second Quantization (in Russian). Nauka, Moscow (1965) (English transl.: Academic Press, New York (1966)) · Zbl 0131.44805 [3] Chevalley, C.: The algebraic theory of spinors and Clifford algebras (collected works, vol. 2). Springer, Berlin (1997) · Zbl 0899.01032 [4] Fauser, B.: A Treatise on Quantum Clifford Algebras. arXiv:math/0202059 · Zbl 1051.15022 [5] Korepanov, I.G., Sadykov, N.M.: Parameterizing the simplest Grassmann-Gaussian relations for Pachner move 3-3. SIGMA 9, paper 053 (2013). arXiv:1305.3246 · Zbl 1288.15033 [6] Korepanov, I.G.: Two-cocycles give a full nonlinear parameterization of the simplest 3-3 relation. Lett. Math. Phys. 104(10), 1235-1261 (2014). arXiv:1310.4075 · Zbl 1327.15057 [7] Korepanov, I.G.: Multiplicative expression for the coefficient in fermionic 3-3 relation. Mathematics 4(1), paper 3 (2016). doi:10.3390/math4010003. arXiv:1503.02272 · Zbl 1343.57014 [8] Korepanov, I.G.: Free fermions on a piecewise linear four-manifold. II: Pachner moves (2017, work in progress) · Zbl 1409.57025 [9] Lickorish, W.B.R.: Simplicial moves on complexes and manifolds. Geom. Topol. Monogr. 2, 299-320 (1999). arXiv:math/9911256 · Zbl 0963.57013 [10] Pachner, U.: PL homeomorphic manifolds are equivalent by elementary shellings. Eur. J. Comb. 12, 129-145 (1991) · Zbl 0729.52003 [11] Turaev, V.G.: Introduction to Combinatorial Torsions. Birkhäuser, Basel (2001) · Zbl 0970.57001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.