2011/05/31 by I. G. Korepanov, Igor G. Korepanov · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic number #Algebraic structure #Boundary (topology) #Geometric and Algebraic Topology #Grassmannian #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Piecewise #Pure mathematics #Symbolic computation #math-ph #math.AT #math.MP #math.QA
paper · pdf · doi:10.3842/sigma.2011.117
published as SIGMA 7 (2011), 117, 23 pages
arxiv created 2011/12/18 · openalex publication_date 2011/12/18 · arxiv updated 2011/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally -using symbolic computer calculations; their essential new feature is that, although they can be treated as deformations of relations corresponding to torsions of acyclic complexes, they can no longer be explained in such terms. In the simpler case of three dimensions, we define an invariant, based on our relations, of a piecewise-linear manifold with triangulated boundary, and present example calculations confirming its nontriviality.