I expressed several times the belief that sub-riemannian geometry represents an example of a mathematically new phenomenon, which I call “non-commutative analysis”. Repeatedly happened that apparently general results simply don’t work well when applied to sub-riemannian geometry. 332 more words

## Tags » Spaces With Dilations

#### A less understood problem in sub-riemannian geometry (I)

A complete, locally compact riemannian manifold is a length metric space by the Hopf-Rinow theorem. The problem of intrinsic characterization of riemannian spaces asks for the recovery of the manifold structure and of the riemannian metric from the distance function coming from to the length functional. 871 more words

#### Dictionary from emergent algebra to graphic lambda calculus (III)

Continuing from Dictionary from emergent algebra to graphic lambda calculus (II) , let’s introduce the following macro, which is called “relative gate”:

If this macro looks involved, then we might express it with the help of… 471 more words

#### Dictionary from emergent algebra to graphic lambda calculus (II)

This post continues the Dictionary from emergent algebra to graphic lambda calculus (I). Let us see if we can prove the approximate associativity property (for the approximate sum) in… 428 more words

#### Dictionary from emergent algebra to graphic lambda calculus (I)

Because I am going to explore in future posts the emergent algebra sector, I think it is good to know where we stand with using… 1,251 more words

#### What group is this? (Parallel transport in spaces with dilations, II)

I continue from Parallel transport in spaces with dilations, I. Recall that we have a set , which could be see as the complete directed graph . 385 more words

#### Parallel transport in spaces with dilations, I

I intended to call this series of posts “What group is this?”, but I switched to this more precise, albeit more bland name. In this first post of the series I take again, in more generality, the construction explained in the post 824 more words