2005/12/21 by John R. Klein, E. Bruce Williams · 22 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Computer science #Fixed-point theorem #Geometric and Algebraic Topology #Geometry #Homotopy #Homotopy and Cohomology in Algebraic Topology #Intersection (aeronautics) #Intersection theory #Mathematical analysis #Mathematical proof #Mathematics #Point (geometry) #Pure mathematics #Space (punctuation) #math.AT #math.GT #msc:55N45 #msc:57R19
paper · pdf · doi:10.2140/gt.2007.11.939
published in Geometry & Topology 11(2), 939-977 (Mathematical Sciences Publishers)
arxiv created 2005/12/21 · openalex publication_date 2007/05/30 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a new approach to intersection theory. Our "cycles" are closed manifolds mapping into compact manifolds and our "intersections" are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn [17], but our proofs are fundamentally different.