Presentation of homotopy types under a space

Published 26 May 2010 in math.AT | (1005.4810v1)

Abstract: We compare the structure of a mapping cone in the category Top^D of spaces under a space D with differentials in algebraic models like crossed complexes and quadratic complexes. Several subcategories of Top^D are identified with algebraic categories. As an application we show that there are exactly 16 essential self--maps of S² x S² fixing the diagonal.

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