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A geometry of information, I: Nerves, posets and differential forms.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNConference contribution/Paper

Published
Publication date27/08/2005
Host publicationSpatial Representation
EditorsRalph Kopperman, Michael Smyth, Dieter Spreen, Julian Webster
PublisherIBFI, Schloss Dagstuhl, Germany
Volume04351
<mark>Original language</mark>English

Publication series

NameDagstuhl Seminar Proceedings
PublisherIBFI, Schloss Dagstuhl, Germany

Abstract

The main theme of this workshop is ‘Spatial Representation: Continuous vs. Discrete’. Spatial representation has two contrasting but interacting aspects (i) representation of spaces’ and (ii) representation by spaces. In this paper, we will examine two aspects that are common to both interpretations of the theme, namely nerve constructions and refinement. Representations change, data changes, spaces change. We will examine the possibility of a ‘differential geometry’ of spatial representations of both types, and in the sequel give an algebra of differential forms that has the potential to handle the dynamical aspect of such a geometry. We will discuss briefly a conjectured class of spaces, generalising the Cantor set which would seem ideal as a test-bed for the set of tools we are developing.

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