August 26, 2024Open Access

Morse theory in definably complete d-minimal structures

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Abstract

Consider a definable complete d-minimal expansion (F, <, +, , 0, 1, , ) of an oredered field F. Let X be a definably compact definably normal definable Cʳ manifold and 2 r <. We prove that the set of definable Morse functions is open and dense in the set of definable Cʳ functions on X with respect to the definable C² topology.

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Fujita et al. (Mon,) studied this question.

synapsesocial.com/papers/68e5b010b6db643587549375 https://doi.org/https://doi.org/10.48550/arxiv.2408.14675

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