Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 1 (2005), 021, 7 pages      math.GT/0510095      https://doi.org/10.3842/SIGMA.2005.021

Pachner Move 3 –> 3 and Affine Volume-Preserving Geometry in R3

Igor G. Korepanov
South Ural State University, 76 Lenin Ave., 454080 Chelyabinsk, Russia

Received October 06, 2005, in final form November 21, 2005; Published online November 24, 2005

Abstract
Pachner move 3 –> 3 deals with triangulations of four-dimensional manifolds. We present an algebraic relation corresponding in a natural way to this move and based, a bit paradoxically, on three-dimensional geometry.

Key words: piecewise-linear topology; Pachner move; algebraic relation; three-dimensional affine geometry.

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