COMPUTABILITY OF HOMOTOPY GROUPS OF NILPOTENT COMPLEXES.

Title: COMPUTABILITY OF HOMOTOPY GROUPS OF NILPOTENT COMPLEXES.
Identifier: AAI8501183
identifier: 8501183
Creator: WELD, KATHRYN.
Contributor: Eldon Dyer
Date: 1984
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In this paper we prove that if X is a nilpotent connected simplicial set which is finite in each dimension then (n (GREATERTHEQ) 2) (pi)(,n)X is a finitely generated abelian group. We define recursive simplicial sets and maps and prove that there is an effective procedure for constructing the Postnikov tower of X as a tower of recursive simplicial sets and maps. Moreover, there are effective procedures for producing for (pi)(,n)X, n (GREATERTHEQ) 2, a recursively enumerable abelian group presentation and, for n > 1, finite abelian group presentations of (GAMMA)(,i)(pi)(,n)X/(GAMMA) (,i+1)(pi)(,n)X, where (GAMMA)(,1)(pi)(,n)X = (pi)(,n)X (GREATERTHEQ) (GAMMA)(,2)(pi)(,n)X (GREATERTHEQ) ... (GREATERTHEQ) (GAMMA)(,c+1)(pi)(,n)X = {lcub}1{rcub} is the lower central series of the nilpotent action of (pi)(,1)X on (pi)(,n)X.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.
Program: Mathematics