JournalsjemsVol. 9 , No. 4DOI 10.4171/jems/99

A general Fredholm theory I: a splicing-based differential geometry

  • Helmut W. Hofer

    Institute for Advanced Study, Princeton, USA
  • Kris Wysocki

    Penn State University, University Park, United States
  • Eduard Zehnder

    ETH Zürich, Switzerland
A general Fredholm theory I: a splicing-based differential geometry cover

Abstract

This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. These spaces, in general, are locally not homeomorphic to open sets in Banach spaces. The present paper describes some of the differential geometry of this new class of spaces. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory, and Symplectic Field Theory.