1961/04/01 by Michael Atiyah · 3 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology #Algebraic structures and combinatorial models #Cobordism #Exact sequence #Mathematics #Cohomology #Sequence (biology) #Pure mathematics #Space (punctuation) #Type (biology) #Topology (electrical circuits) #Combinatorics #Computer science
paper · doi:10.1017/s0305004100035064
openalex publication_date 1961/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/06
In (10), (11) Wall determined the structure of the cobordism ring introduced by Thom in (9). Among Wall's results is a certain exact sequence relating the oriented and unoriented cobordism groups. There is also another exact sequence, due to Rohlin(5), (6) and Dold(3) which is closely connected with that of Wall. These exact sequences are established by ad hoc methods. The purpose of this paper is to show that both these sequences are ‘cohomology-type’ exact sequences arising in the well-known way from mappings into a universal space. The appropriate ‘cohomology’ theory is constructed by taking as universal space the Thom complex MSO ( n ), for n large. This gives rise to (oriented) cobordism groups MSO *( X ) of a space X .