Rational obstruction theory and rational homotopy sets |
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Authors: | Martin Arkowitz Gregory Lupton |
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Affiliation: | (1) Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA (e-mail: Martin.Arkowitz@dartmouth.edu), US;(2) Department of Mathematics, Cleveland State University, Cleveland, OH 44115, USA (e-mail: Lupton@math.csuohio.edu), US |
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Abstract: | We develop an obstruction theory for homotopy of homomorphisms between minimal differential graded algebras. We assume that has an obstruction decomposition given by and that f and g are homotopic on . An obstruction is then obtained as a vector space homomorphism . We investigate the relationship between the condition that f and g are homotopic and the condition that the obstruction is zero. The obstruction theory is then applied to study the set of homotopy classes . This enables us to give a fairly complete answer to a conjecture of Copeland-Shar on the size of the homotopy set [A,B] whenA and B are rational spaces. In addition, we give examples of minimal algebras (and hence of rational spaces) that have few homotopy classes of self-maps. Received February 22, 1999; in final form July 7, 1999 / Published online September 14, 2000 |
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Keywords: | Mathematics Subject Classification (1991): 55P62 55Q05 55S35 55P10 |
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