Diagram Geometry by Francis Buekenhout & Arjeh M. Cohen

Author:Francis Buekenhout & Arjeh M. Cohen
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

This number is −1 if and only if the four points form a harmonic quadruple. The definition extends to a cross-ratio for any four points on the projective line . For a=0 and b=∞ (so that the corresponding point is (1:0)=∞), the cross-ratio is the scalar λ by which c needs to be multiplied to obtain d as the image of c under a perspectivity with center a and hyperplane b (so the unique element of π(a,b) mapping c to d is identified with multiplication by λ). This theory is classical; see [4, 167].

The harmonic quadruples determine the full line structure provided that −1 is different from 1, so the definition of a projective line could have been given in terms of harmonic quadruples rather than regular groups.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.