Journal d’Analyse Mathematique

, Volume 76, Issue 1, pp 289–319 | Cite as

Degree theory forC 1 Fredholm mappings of index 0



We develop a degree theory forC 1 Fredholm mappings of index 0 between Banach spaces and Banach manifolds. As in earlier work devoted to theC 2 case, our approach is based upon the concept of parity of a curve of linear Fredholm operators of index 0. This avoids considerations about Fredholm structures involved in other approaches and leads to a theory as complete as that of Leray-Schauder in a much broader setting. In particular, the well-known possible sign change under homotopy is fully elucidated. The technical difficulty arising withC 1 versusC 2 Fredholm mappings of index 0 is notorious: with onlyC 1 smoothness, the Sard-Smale theorem is no longer available to handle crucial issues involving homotopy. In this work, this difficulty is overcome by using a new approximation theorem forC 1 Fredholm mappings of arbitrary index instead of the Sard—Smale theorem when dealing with homotopies.


Banach Space Base Point Real Banach Space Degree Theory Homotopy Invariance 
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© Hebrew University of Jerusalem 1998

Authors and Affiliations

  1. 1.Dipartimento di matematicaPolitecnico di TorinoTorinoItaly
  2. 2.Department of MathematicsUniversity of PittsburghPittsburghUSA

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