1997/12/21 by Allen Hatcher, Darryl McCullough · 27 citations
Computer Science · Mathematics · #Abelian group #Boundary (topology) #Class (philosophy) #Classifying space #Covering space #Diffeomorphism #Fundamental group #Geometric and Algebraic Topology #Group (periodic table) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Identity (music) #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Space (punctuation) #Topological and Geometric Data Analysis #math.GT #msc:55R35 #msc:57M99 #msc:58D99
paper · pdf · doi:10.2140/gt.1997.1.91
published in Geometry & Topology 1(1), 91-109 (Mathematical Sciences Publishers) · 19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper7.abs.html
arxiv created 1997/12/21 · openalex publication_date 1997/12/21 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The main theorem shows that if M is an irreducible compact connected orientable 3-manifold with non-empty boundary, then the classifying space BDiff (M rel M ) of the space of diffeomorphisms of M which restrict to the identity map on M has the homotopy type of a finite aspherical CW-complex. This answers, for this class of manifolds, a question posed by M Kontsevich. The main theorem follows from a more precise result, which asserts that for these manifolds the mapping class group H(M rel M ) is built up as a sequence of extensions of free abelian groups and subgroups of finite index in relative mapping class groups of compact connected surfaces.