The realization space of a II-algebra: A moduli problem in algebraic topology

D. Blanc, W. G. Dwyer, P. G. Goerss

Research output: Contribution to journalArticlepeer-review


A II-algebra A is a graded group with all of the algebraic structure possessed by the homotopy groups of a pointed connected topological space. We study the moduli space R(A) of realizations of A, which is defined to be the disjoint union, indexed by weak equivalence classes of CW-complexes X with π*(X)=A, of the classifying space of the monoid of self homotopy equivalences of X. Our approach amounts to a kind of homotopical deformation theory: we obtain a tower whose homotopy limit is R(A), in which the space at the bottom is BAut(A) and the successive fibres are determined by II-algebra cohomology. (This cohomology is the analog for II-algebras of the Hochschild cohomology of an associative ring or the André-Quillen cohomology of a commutative ring.) It seems clear that the deformation theory can be applied with little change to study other moduli problems in algebra and topology.

Original languageEnglish
Pages (from-to)857-892
Number of pages36
Issue number4
StatePublished - Jul 2004


  • Classification
  • Moduli
  • Realization

ASJC Scopus subject areas

  • Geometry and Topology


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