Analogues of the Atiyah-Wall exact sequences for cobordism groups of singular maps
András Csépai
Journal of Singularities
volume 26 (2023), 128-169
Received: 29 May 2023. Received in revised form: 31 October 2023.
Abstract:
Classical results of Rohlin, Dold, Wall and Atiyah yield two exact sequences that connect the cobordism groups of oriented and unoriented manifolds. In this paper we present analogous exact sequences connecting the oriented and unoriented cobordism groups of maps with prescribed singularities. This gives positive answer to a fifteen-year-old question posed by Szűcs and has interesting consequences even in the case of cobordisms of immersions.
2020 Mathematical Subject Classification:
57R90 (Primary), 57R35, 57R45, 55N22, 55P42 (Secondary)
Key words and phrases:
cobordism, singular maps, exact sequences
Author(s) information:
András Csépai
Eötvös Loránd University
Institute of Mathematics
Pázmány Péter sétány 1/c
Budapest, H-1117 Hungary
email: csepai.andras112358@gmail.com