Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
A polyfold proof of the Arnold conjecture. |
| Συγγραφείς: |
Filippenko, Benjamin, Wehrheim, Katrin |
| Πηγή: |
Selecta Mathematica, New Series; Feb2022, Vol. 28 Issue 1, p1-73, 73p |
| Θεματικοί όροι: |
Symplectic manifolds, Logical prediction |
| Περίληψη: |
We give a detailed proof of the homological Arnold conjecture for nondegenerate periodic Hamiltonians on general closed symplectic manifolds M via a direct Piunikhin–Salamon–Schwarz morphism. Our constructions are based on a coherent polyfold description for moduli spaces of pseudoholomorphic curves in a family of symplectic manifolds degenerating from C P 1 × M to C + × M and C - × M , as developed by Fish–Hofer–Wysocki–Zehnder as part of the Symplectic Field Theory package. To make the paper self-contained we include all polyfold assumptions, describe the coherent perturbation iteration in detail, and prove an abstract regularization theorem for moduli spaces with evaluation maps relative to a countable collection of submanifolds. The 2011 sketch of this proof was joint work with Peter Albers, Joel Fish. [ABSTRACT FROM AUTHOR] |
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