preprint: "Ordinary and directed combinatorial homotopy,..."

preprint: "Ordinary and directed combinatorial homotopy,..."

[Marco Grandis]

The following paper is available in ps and ps.gz. 

It is about my talk at:
'Conference on Algebraic Topological Methods in Computer Science'
Stanford, July 30 - August 3, 2001.


'Ordinary and directed combinatorial homotopy,
applied to image analysis and concurrency'
Marco Grandis

Abstract. Combinatorial homotopical tools developed in previous works, and
consisting essentially of intrinsic homotopy theories for simplicial
complexes and directed simplicial complexes, can be applied to explore
mathematical models representing images, or directed images, or concurrent
processes.

        An image, represented by a metric space  X,  can be explored at a
variable resolution  e > 0,  by equipping it with a structure  t_eX  of
simplicial complex depending on  e;  this complex can be further analysed
by homotopy groups   \pi^e_n(X) = \pi_n(t_eX)   and homology groups
H^e_n(X) = H_n(t_eX).   Loosely speaking, these objects detect
singularities which can be captured by an n-dimensional grid, with edges
bound by  e;  this works equally well for continuous or discrete regions of
euclidean spaces.

        Similarly, a directed image, represented by an 'asymmetric metric
space', produces a family of directed simplicial complexes  f_eX  and can
be explored by the fundamental n-category of the latter. The same directed
tools can be applied to mathematical models of concurrent automata, like
Chu-spaces.

AVAILABLE AT:

ftp://www.dima.unige.it/Home/grandis/public/Cmb.App.ps
ftp://www.dima.unige.it/Home/grandis/public/Cmb.App.ps.gz

(18p, 260K)


*****

With best regards

        Marco Grandis

Dipartimento di Matematica
Universita' di Genova
via Dodecaneso 35
16146 GENOVA, Italy

e-mail: grandis@dima.unige.it
tel: +39.010.353 6805   fax: +39.010.353 6752

http://www.dima.unige.it/~grandis/
ftp://www.dima.unige.it/Home/grandis/public/







 1-Oct-2001 18:40:07 -0300,1032;000000000000-0000002b