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

Authors: Jonathan Gratus and Timothy Porter

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)

Abstract

The main theme of this workshop is 'Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation \emph{of} spaces' and (ii) representation \emph{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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Jonathan Gratus and Timothy Porter. A geometry of information, I: Nerves, posets and differential forms. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{gratus_et_al:DagSemProc.04351.6,
  author =	{Gratus, Jonathan and Porter, Timothy},
  title =	{{A geometry of information, I: Nerves, posets and differential forms}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.6},
  URN =		{urn:nbn:de:0030-drops-1268},
  doi =		{10.4230/DagSemProc.04351.6},
  annote =	{Keywords: Chu spaces , nerves , differential forms}
}

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DOI: 10.4230/DagSemProc.04351.7

A geometry of information, II: Sorkin models, and biextensional collapses

Authors: Jonathan Gratus and Timothy Porter

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)

Abstract

In this second part of our contribution to the workshop, we look in more detail at the Sorkin model, its relationship to constructions in Chu space theory, and then compare it with the Nerve constructions given in the first part.

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Jonathan Gratus and Timothy Porter. A geometry of information, II: Sorkin models, and biextensional collapses. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{gratus_et_al:DagSemProc.04351.7,
  author =	{Gratus, Jonathan and Porter, Timothy},
  title =	{{A geometry of information, II: Sorkin models, and biextensional collapses}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.7},
  URN =		{urn:nbn:de:0030-drops-1271},
  doi =		{10.4230/DagSemProc.04351.7},
  annote =	{Keywords: Chu space , Sorkin model , Nerve}
}

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Documents authored by Gratus, Jonathan

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

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A geometry of information, II: Sorkin models, and biextensional collapses

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