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 language | English |
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Pages (from-to) | 585-621 |
Number of pages | 37 |
Journal | Topological methods in nonlinear analysis |
Volume | 59 |
Issue number | 2A |
Early online date | 30 Jan 2022 |
DOIs | |
Publication status | Published - 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