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Full-Text Articles in Applied Mathematics
Higher Homotopy Operations And André-Quillen Cohomology, David Blanc, Mark W. Johnson, James M. Turner
Higher Homotopy Operations And André-Quillen Cohomology, David Blanc, Mark W. Johnson, James M. Turner
University Faculty Publications and Creative Works
There are two main approaches to the problem of realizing a Π-algebra (a graded group Λ equipped with an action of the primary homotopy operations) as the homotopy groups of a space X. Both involve trying to realize an algebraic free simplicial resolution G . of Λ by a simplicial space W ., and proceed by induction on the simplicial dimension. The first provides a sequence of André-Quillen cohomology classes in H n+2(Λ;Ω nΛ) (n≥1) as obstructions to the existence of successive Postnikov sections for W . (cf. Dwyer et al. (1995) [27]). The second gives a sequence of geometrically …
Higher Homotopy Operations And Cohomology, David Blanc, Mark W. Johnson, James M. Turner
Higher Homotopy Operations And Cohomology, David Blanc, Mark W. Johnson, James M. Turner
University Faculty Publications and Creative Works
We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams. © 2010 ISOPP.