1966/01/01 by John Milnor · 496 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Nuclear Structure and Function #Congenital limb and hand anomalies #Hedgehog Signaling Pathway Studies #Torsion (gastropod) #Mathematics #Pure mathematics #Medicine #Anatomy
paper · pdf · doi:10.1090/s0002-9904-1966-11484-2
published in Bulletin of the American Mathematical Society 72(3), 358-426 (American Mathematical Society)
openalex publication_date 1966/01/01 · openalex created_date 2022/02/24 · openalex updated_date 2026/07/07
In 1935, Reidemeister, Franz and de Rham introduced the concept of "torsion" for certain finite simplicial complexes. For example let X be a finite complex whose fundamental group TTIX is cyclic of order m. We can identify TT\X with the group of covering transformations of the universal covering complex X. If ir\X operates trivially on the rational homology H*(X @), then the torsion of X is defined as a certain collection of elements in the algebraic number field Q [exp(27ri/m)]. This torsion is a kind of determinant which describes the way in which the simplexes of X are fitted together with respect to the action of ir\X. The actual definition will be given in 8. (See Franz [1935