THE HOMOTOPY CLASSIFICATION OF PROPER FREDHOLM MAPS OF INDEX ONE

Alberto Abbondandolo, Thomas Rot

Research output: Contribution to JournalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)585-621
Number of pages37
JournalTopological methods in nonlinear analysis
Volume59
Issue number2A
Early online date30 Jan 2022
DOIs
Publication statusPublished - Jun 2022

Bibliographical note

Funding Information:
2020 Mathematics Subject Classification. 58B05, 58B15, 57R90, 47A53, 47H11. Key words and phrases. Fredholm maps; Pontryagin–Thom construction; framed cobordism. The research of A. Abbondandolo is supported by the DFG-Project 380257369 “Morse theoretical methods in Hamiltonian dynamics”. The research of T.O. Rot is supported by NWO-NWA Startimpuls – 400.17.608.

Publisher Copyright:
© 2022 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University in Toruń.

Funding

2020 Mathematics Subject Classification. 58B05, 58B15, 57R90, 47A53, 47H11. Key words and phrases. Fredholm maps; Pontryagin–Thom construction; framed cobordism. The research of A. Abbondandolo is supported by the DFG-Project 380257369 “Morse theoretical methods in Hamiltonian dynamics”. The research of T.O. Rot is supported by NWO-NWA Startimpuls – 400.17.608.

Keywords

  • framed cobordism
  • Fredholm maps
  • Pontryagin–Thom construction

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