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2answers
381 views

Are exotic spheres still exotic in generalised smooth spaces?

This is really more of a philosophical question, and the title is somewhat rhetorical: Exotic spheres are a feature of smooth manifold theory, where certain spheres can have more than one ...
1
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2answers
180 views

are immersions/submersions captured in generalised smooth spaces by some universal property?

Immersions & sumersions are important in differential manifolds. They rely on their definition of the construction of the tangent bundle. I realise that generalised smooth spaces do not have a ...
3
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0answers
190 views

Regular maps between Frechet manifolds and pullbacks

An oft-used example of a regular map of finite-dimensional smooth manifolds is a submersion. We have the well-known result that the pullback of a submersion exists and is a submersion. For Frechet ...
3
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1answer
179 views

Can ordinary schemes be described as sheves of algebras/models for a certain Lawvere theory?

Consider the definition of a $\mathcal{C}^{\infty}$-scheme given in Dominique Joyce's "Algebraic geometry over C-infty rings". As far as I uderstand (not being an expert either in C-infty rings nor in ...
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2answers
775 views

Nice application of generalized smooth spaces

I am a fan of category theory in general, and I appreciate that various brands of generalized smooth spaces (Diffeological spaces, Chen spaces, Frolicher spaces ...) form much nicer categories of ...