This article is cited in 10 papers

Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: II. An Algebraic Complex and Moves $2\leftrightarrow 4$

I. G. Korepanov

South Ural State University

Abstract: We present sequences of linear maps of vector spaces with fixed bases. Each term of a sequence is a linear space of differentials of metric values ascribed to the elements of a simplicial complex determining a triangulation of a manifold. If a sequence is an acyclic complex, then we can construct a manifold invariant using its torsion. We demonstrate this first for three-dimensional manifolds and then construct the part of this program for four-dimensional manifolds pertaining to moves $2\leftrightarrow 4$.

Keywords: piecewise-linear manifolds, manifold invariants Pachner moves, differential identities for Euclidean simplices, acyclic complexes.

Received: 04.02.2002

DOI: 10.4213/tmf378

 English version: Theoretical and Mathematical Physics, 2002, 133:1, 1338–1347

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