The homotopy classification of proper Fredholm maps of index one

Alberto Abbondandolo; Thomas O. Rot

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arXiv · 2005.03936

The homotopy classification of proper Fredholm maps of index one

Alberto Abbondandolo·Thomas O. Rot

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Abstract

In a previous paper we classified the homotopy classes of proper Fredholm maps from an infinite dimensional Hilbert manifold to its model space in terms of a suitable version of framed cobordism. We explicitly computed these homotopy classes for non-positive index. In this paper we compute the homotopy classes of proper Fredholm maps of index one from a simply connected Hilbert manifold to its model space. This classification uses a new numerical invariant for proper Fredholm maps of index one.

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Alberto Abbondandolo, Thomas O. Rot. 2020-05-08. The homotopy classification of proper Fredholm maps of index one. https://arxiv.org/abs/2005.03936

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