HOMOTOPY

Charles François (2004). HOMOTOPY, International Encyclopedia of Systems and Cybernetics, 2(1): 1583.

Collection	International Encyclopedia of Systems and Cybernetics
Year	2004
Vol. (num.)	2(1)
ID	◀ 1583 ▶
Object type	Methodology or model

Property of two paths in a topological space that can be deduced from each other by continuous deformation.

The main interest of this concept is to allow for comparisons between forms which could seem at first sight unrelated.

Homotopic deformation has been extensively used by d'Arcy W. THOMPSON in his famous work “On growth and form” (1916, 1952). THOMPSON applied it to comparative anatomy and phyllotaxy, but also to the mechanical structures in bridges and other constructions and, generally, to the study of the relations between forms.

Homotopy is a special case of homeomorphism and isomorphisms