2004/02/08 by Haibao Duan, Duan, Haibao, Shicheng Wang +1 · 1 citation
Mathematics · #55M25 #57R19 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:55M25 #msc:57R19
paper · pdf · doi:10.48550/arxiv.math/0402119
18 pages
arxiv created 2004/02/08 · openalex publication_date 2004/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Thom-Pontrjagin constructions are used to give a computable necessary and sufficient condition when a homomorphism ϕ: Hn(L;Z)→ Hn(M;Z) can be realized by a map f:M→ L of degree k for closed (n-1)-connected 2n-manifolds M and L, n>1. A corollary is that each (n-1)-connected 2n-manifold admits selfmaps of degree larger than 1, n>1. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree k map from a closed orientable 4-manifold M to a closed simply connected 4-manifold L in terms of their intersection forms, in particular there is a map f:M→ L of degree 1 if and only if the intersection form of L is isomorphic to a direct summand of that of M.