Geodesic
Analogues of the Atiyah-Wall exact sequences for cobordism groups of singular maps
Journal of Singularities, Tome 26 (2023), pp. 128-169

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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.
DOI : 10.5427/jsing.2023.26g
Classification : 57R90(), 57R35, 57R45, 55N22, 55P42() 
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     author = {Andr\'as Cs\'epai},
     title = {Analogues of the {Atiyah-Wall} exact sequences for cobordism groups of singular maps},
     journal = {Journal of Singularities},
     pages = {128--169},
     publisher = {mathdoc},
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     doi = {10.5427/jsing.2023.26g},
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András Csépai. Analogues of the Atiyah-Wall exact sequences for cobordism groups of singular maps. Journal of Singularities, Tome 26 (2023), pp. 128-169. doi: 10.5427/jsing.2023.26g

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