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

Physics

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper

Published

Standard

A geometry of information, I: Nerves, posets and differential forms. / Gratus, Jonathan; Porter, Timothy.
Spatial Representation. ed. / Ralph Kopperman; Michael Smyth; Dieter Spreen; Julian Webster. Vol. 04351 IBFI, Schloss Dagstuhl, Germany, 2005. (Dagstuhl Seminar Proceedings).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper

Harvard

Gratus, J & Porter, T 2005, A geometry of information, I: Nerves, posets and differential forms. in R Kopperman, M Smyth, D Spreen & J Webster (eds), Spatial Representation. vol. 04351, Dagstuhl Seminar Proceedings, IBFI, Schloss Dagstuhl, Germany. https://doi.org/10.4230/DagSemProc.04351.6

APA

Gratus, J., & Porter, T. (2005). A geometry of information, I: Nerves, posets and differential forms. In R. Kopperman, M. Smyth, D. Spreen, & J. Webster (Eds.), Spatial Representation (Vol. 04351). (Dagstuhl Seminar Proceedings). IBFI, Schloss Dagstuhl, Germany. https://doi.org/10.4230/DagSemProc.04351.6

Vancouver

Gratus J, Porter T. A geometry of information, I: Nerves, posets and differential forms. In Kopperman R, Smyth M, Spreen D, Webster J, editors, Spatial Representation. Vol. 04351. IBFI, Schloss Dagstuhl, Germany. 2005. (Dagstuhl Seminar Proceedings). doi: 10.4230/DagSemProc.04351.6

Author

Gratus, Jonathan ; Porter, Timothy. / A geometry of information, I: Nerves, posets and differential forms. Spatial Representation. editor / Ralph Kopperman ; Michael Smyth ; Dieter Spreen ; Julian Webster. Vol. 04351 IBFI, Schloss Dagstuhl, Germany, 2005. (Dagstuhl Seminar Proceedings).

Bibtex

@inproceedings{7756a6f3f67f45fb80443bfc8b284063,

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

abstract = "The main theme of this workshop is {\textquoteleft}Spatial Representation: Continuous vs. Discrete{\textquoteright}. Spatial representation has two contrasting but interacting aspects (i) representation of spaces{\textquoteright} 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 {\textquoteleft}differential geometry{\textquoteright} 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.",

keywords = "Chu spaces, nerves, differential forms",

author = "Jonathan Gratus and Timothy Porter",

note = "DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.",

year = "2005",

month = aug,

day = "27",

doi = "10.4230/DagSemProc.04351.6",

language = "English",

volume = "04351",

series = "Dagstuhl Seminar Proceedings",

publisher = "IBFI, Schloss Dagstuhl, Germany",

editor = "Ralph Kopperman and Michael Smyth and Dieter Spreen and Julian Webster",

booktitle = "Spatial Representation",

}

RIS

TY - GEN

T1 - A geometry of information, I: Nerves, posets and differential forms.

AU - Gratus, Jonathan

AU - Porter, Timothy

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2005/8/27

Y1 - 2005/8/27

N2 - 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.

AB - 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.

KW - Chu spaces

KW - nerves

KW - differential forms

U2 - 10.4230/DagSemProc.04351.6

DO - 10.4230/DagSemProc.04351.6

M3 - Conference contribution/Paper

VL - 04351

T3 - Dagstuhl Seminar Proceedings

BT - Spatial Representation

A2 - Kopperman, Ralph

A2 - Smyth, Michael

A2 - Spreen, Dieter

A2 - Webster, Julian

PB - IBFI, Schloss Dagstuhl, Germany

ER -

Research

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