On the homotopy classification of proper Fredholm maps into a Hilbert space

Alberto Abbondandolo, Thomas O. Rot

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Abstract

We classify the homotopy classes of proper Fredholm maps from an infinitedimensional Hilbert manifold into its model space in terms of a suitable version of framed cobordism. Our construction is an alternative approach to the classification introduced by Elworthy and Tromba in 1970 and does not make use of further structures on the ambient manifold, such as Fredholm structures. In the special case of index zero, we obtain a complete classification involving the Caccioppoli-Smale mod 2 degree and the absolute value of the oriented degree.

Original languageEnglish
Pages (from-to)161-200
Number of pages40
JournalJournal für die reine und angewandte Mathematik
Volume2020
Issue number759
Early online date28 Jan 2018
DOIs
Publication statusPublished - Feb 2020

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