[Alta-Logic] Peripatetic Seminar Friday 14:00 in ICT 616

[Matthew Burke]

Speaker: Jonathan Gallagher

Time and Location: 14:00 9th Mar in ICT 616

Title: Frolicher spaces, Weil spaces, Diffeological spaces and abstract
differential geometry

Abstract: In differential geometry, obtaining a smooth structure on
spaces of smooth maps is a motivation for the introduction of various
kinds of generalized smooth spaces. Frechet manifolds do allow a
manifold structure on the space of smooth maps between *finite*
dimensional smooth manifolds, but the category is not cartesian closed.
Frolicher spaces, Weil spaces, and diffeological spaces all have the
advantage that they generalize smooth manifolds, and are cartesian
closed categories.

We will describe these categories as Tangent categories. They are *not*
tangent categories, but they should be. We will introduce a notion of
generalized microlinearity, based on the work of Nishimura, whose notion
was based on the work of Wraith and Kock, to extract a tangent full
subcategory.

http://peripatetic-seminar.cpsc.ucalgary.ca/wp/