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Computational homology of n-types

Le, Van Luyen
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2014-01-10
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Homotopy theory, Computational algebra, Mathematics
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Thesis
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Abstract
An n-type X is a CW-space with homotopy groups \pi_iX=0 for all i>n. Up to homotopy equivalence such a space can be specified algebraically by means of a simplicial group whose Moore complex is trivial in degrees >= n. For the case n=2, Mac Lane and Whitehead [1950] showed that there is a one-one correspondence between 2-types and quasi-isomorphism classes of crossed modules. The main goal of this PhD thesis is the development of computational tools for helping with the classification of 2-types. Our primary computational tool is the homology, and persistent homology, of 2-types. We provide a classification of most of the 2-types of order m <= 255.
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PhD fellowship, NUI Galway
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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University of Galway Theses (PhD Theses)