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Homotopy Spheres in Formal Language
Author(s) -
Farmer Frank D.
Publication year - 1982
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1982662171
Subject(s) - mathematics , homotopy , contractible space , homotopy sphere , spheres , homology (biology) , combinatorics , regular homotopy , n connected , homotopy group , pure mathematics , connected component , bounded function , mathematical analysis , physics , biochemistry , chemistry , astronomy , gene
The set of nonempty proper subwords of a word is either contractible or a homotopy n ‐sphere. There is a simple algorithm which computes n . The existence of spherical words is investigated, and the words which yield spheres are determined. A language which is closed under subwords has a finite number of components, and each component has a finitely generated fundamental group. For each n greater than 1, there is a language on two letters which has the homotopy type of an infinite cluster of n ‐sphere. There is a language on two letters which has nontrivial homology in each dimension greater than 1. If a language is closed under subwords and has bounded period, then it has the homotopy type of a finite polyhedron.