Diffeological Submanifolds

Yael Karshon, Jordan Watts

Research output: Other contribution

Abstract

Diffeology is a handy tool for exploring differentiability beyond smooth manifolds. In particular, it allows one to equip singular spaces and infinite-dimensional spaces with a convenient smooth structure, using a simple language. From this language comes a simple definition of a diffeological submanifold: a diffeologically smooth injection $f$ from a manifold $S$ into a diffeological space $X$ that induces a bijection between plots of $S$ and $f(S)$. If $X$ is also a manifold, how does this relate to the classical definition(s) of a submanifold? In fact, an open question asks whether a diffeological submanifold is an immersion. In this talk we will see the answer is "no", using an application of Joris' Theorem. This talk will be for a broad audience, and no knowledge of diffeology will be assumed. This is joint work with Yael Karshon and David Miyamoto.
Original languageEnglish
StatePublished - Nov 2020

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