A general Fredholm theory I: a splicing-based differential geometry
Copyright policy )A general Fredholm theory I: a splicing-based differential geometry
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.
- ETH Zurich Switzerland
- Courant Institute of Mathematical Sciences United States
- Pennsylvania State University United States
- Institute for Advanced Study United States
- New York University United States
Mathematics - Differential Geometry, fillers, strong bundles, Banach scales, sc-smoothness, Functional Analysis (math.FA), 46T99, 58B99, 53C99, Mathematics - Functional Analysis, Differential Geometry (math.DG), Mathematics - Symplectic Geometry, Symplectic aspects of Floer homology and cohomology, M-polyfolds, splicing cores, splicings, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, Symplectic Geometry (math.SG), Fredholm structures on infinite-dimensional manifolds, (Semi-) Fredholm operators; index theories
Mathematics - Differential Geometry, fillers, strong bundles, Banach scales, sc-smoothness, Functional Analysis (math.FA), 46T99, 58B99, 53C99, Mathematics - Functional Analysis, Differential Geometry (math.DG), Mathematics - Symplectic Geometry, Symplectic aspects of Floer homology and cohomology, M-polyfolds, splicing cores, splicings, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, Symplectic Geometry (math.SG), Fredholm structures on infinite-dimensional manifolds, (Semi-) Fredholm operators; index theories
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