2009/07/31 by Qayum Khan
Mathematics · #Advanced Combinatorial Mathematics #Cobordism #Combinatorics #Conjecture #Connected sum #Equivalence (formal languages) #Fundamental group #Geometric and Algebraic Topology #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Simply connected space #Uniqueness #math.AT #math.GT #msc:57N13 #msc:57R67
paper · pdf · doi:10.1016/j.topol.2012.08.005
published as Topology and its Applications, Volume 159, Number 16 (2012), 3432--3444 · 14 pages, 1 figure, accepted by Topology and its Applications
arxiv created 2012/08/10 · openalex publication_date 2012/08/24 · arxiv updated 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show, up to h-cobordism, that the existence and uniqueness of connected sum decompositions of oriented 4-dimensional manifolds is an invariant of homotopy equivalence, assuming that the fundamental group of each summand is "good" in the sense of Freedman and Quinn. On a separate note, we observe that the Borel Conjecture is true in dimension 4 up to s-cobordism, assuming that the fundamental group satisfies the Farrell--Jones Conjecture.