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

Autor:	Abbondandolo, Alberto, Rot, Thomas O.
Rok vydání:	2016
Předmět:	Mathematics - Algebraic Topology Mathematics - Functional Analysis Mathematics - Operator Algebras 58B05 58B15 57R90 47A53
Zdroj:	J. Reine Angew. Math. 759 (2020), 161-200
Druh dokumentu:	Working Paper
Popis:	We classify the homotopy classes of proper Fredholm maps from an infinite dimensional 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. Comment: Revision: Corrected typos. Added discussion on weaker regularity and possible generalizations outside the Hilbert space setting. Added examples of non-orientable maps and a homotopy through proper maps that is not a proper homotopy
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1610.07039 Zobrazit plný text záznamu View this record from Arxiv