Some recent advances in SDG

Some recent advances in SDG

[Anders Kock]

Dear all,

Some of my recent contributions to SDG are posted on arXiv:

1) Most recently (Dec. 2016):
"Metric spaces and SDG" (version 3) - a corrected version of a preprint  posted on arxiv:1610.10005 version 1 and 2. (I apologize if anybody has wasted time with the puzzling redundancies and holes in the first two versions!)
This preprint relates SDG with the theory of some metric spaces advanced by  Busemann in the years 1943-1970 (and he called, quite justified,  his theory "Synthetic Differential Geometry" !).

2) Also, I posted on arXiv:1508.04322, "Affine combinations in affine schemes": out of mutual neighbour points in an affine scheme, one can form arbitrary affine combinations. In a different context, this technique was used for many of the constructions in my book Synthetic Geometry of Manifolds (2010).

3) Finally, arXiv:1610.00286 is a survey talk "New methods for old spaces: synthetic differential geometry", presented as an invited contribution to the workshop (and forthcoming book) organized by M. Anel and G. Catren "New spaces in Mathematics and Physics",  Paris IHP 2015.

These three contributions  concentrate on the combinatorial neighbour relation in geometry, and how it carries along with it diffenential-geometric notions, like "touching", "envelopes", ... - without resorting to differential calculus.

Anders Kock

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