beta version of new book available: "Synthetic Geometry of Manifolds"

beta version of new book available: "Synthetic Geometry of Manifolds"

[Anders Kock]

Dear all,

A beta version of my new book "Synthetic Geometry of Manifolds" is
available via my homepage, http://home.imf.au.dk/kock/

This book deals with some classical spaces in differential geometry, namely
the "prolongation spaces" or "neighbourhoods of the diagonal".  These
spaces provides a natural way of describing some of the basic constructions
in local differential geometry, and in fact, is an inviting gate to
differential geometry, and also to some of those differential-geometric
notions that exist in algebraic geometry.

In the present text, the neighbourhoods of the diagonal are dealt
with, and utilized, using the axiomatic method of synthetic
differential geometry; this obviates many of those technical
difficulties, which till now has made the use of these neighbourhoods
rather uninviting.


Some of the specific differential geometric theories dealt with here
are connection theory (notably affine connections), geometric
distributions, differential forms, jet bundles, differentiable
groupoids, differential operators, Riemannian metrics, harmonic maps.

Anders Kock