TY - JOUR
T1 - On the homotopy classification of proper Fredholm maps into a Hilbert space
AU - Abbondandolo, Alberto
AU - Rot, Thomas O.
PY - 2020/2
Y1 - 2020/2
N2 - 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.
AB - 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.
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U2 - 10.1515/crelle-2017-0054
DO - 10.1515/crelle-2017-0054
M3 - Review article
AN - SCOPUS:85041567080
SN - 0075-4102
VL - 2020
SP - 161
EP - 200
JO - Journal für die reine und angewandte Mathematik
JF - Journal für die reine und angewandte Mathematik
IS - 759
ER -