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Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves
Інший ID:
2010 Mathematics Subject Classification: 15A75; 55-04; 57M27, 57Q10; 57R56
DOI: http://dx.doi.org/10.3842/SIGMA.2011.117
DOI: http://dx.doi.org/10.3842/SIGMA.2011.117
Посилання:
Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves / I.G. Korepanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ.
Підтримка:
This paper has been written with partial financial support from Russian Foundation for Basic
Research, Grant no. 10-01-00088-a, and a grant from the Academic Senate of Moscow State
University of Instrument Engineering and Computer Sciences. I also thank the referees for their constructive and helpful comments.
Дата:
2011
Переглядів:
525
Завантажень:
259
Анотація:
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.
