2003/11/03 by Michael A. Mandell · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Eilenberg–MacLane space #Functor #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Mathematics #Nilpotent #Pure mathematics #Type (biology) #math.AT #msc:55P15 #msc:55Q05 #n-connected
paper · pdf · doi:10.1007/s10240-006-0037-6
published as Publ. Math. IHES, 103 (2006), 213-246
arxiv created 2003/11/03 · openalex publication_date 2006/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> algebras is faithful but not full.