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3/3 Boundary, corners, strong bundles, and implicit function theorems

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No logo availableInstitut des Hautes Études Scientifiques (IHÉS)
 Fish, Joel

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3/3 Boundary, corners, strong bundles, and implicit function theorems
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36
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CC Attribution 3.0 Unported:
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In this talk, we generalize the notion of sc-retracts to include cases with boundary and corner structure. In addition, we develop the notion of a strong bundle (of which the Cauchy-Riemann operator is a section) and state an implicit function theorem for transverse Fredholm sections with compact zero-set, which guarantees the zero set of the section is a manifold with boundary and corners, with boundary/corner structure induced from the ambient M-polyfold. [Related literature: Sections 5.2, 5.3, and 6.1 of Polyfolds: A First and Second Look.