The central role of diagrams in algebraic topology

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The great achievement of Cantor and Dedekind in the 19th c. was not the arithmetization of the geometrical line, but rather the use of the notion of set to extend the number system to the reals and the transfinite numbers, and to recast the line as a set of points and numbers systems as sets of numbers: this prepares the ground for the emergence of topology and then algebraic topology in the 20th c. and the novel diagrams that accompany its presentation in the textbook written by Singer and Thorpe.

Original languageEnglish (US)
Title of host publicationDiagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings
EditorsGem Stapleton, Francesco Bellucci, Amirouche Moktefi, Peter Chapman, Sarah Perez-Kriz
PublisherSpringer Verlag
Pages814-816
Number of pages3
ISBN (Print)9783319913759
StatePublished - Jan 1 2018
Event10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 - Edinburgh, United Kingdom
Duration: Jun 18 2018Jun 22 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10871 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Conference on the Theory and Application of Diagrams, Diagrams 2018
CountryUnited Kingdom
CityEdinburgh
Period6/18/186/22/18

Fingerprint

Numbering systems
Algebraic topology
Number system
Diagram
Topology
Textbooks
Line
Cantor
Set of points
Presentation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Grosholz, E. R. (2018). The central role of diagrams in algebraic topology. In G. Stapleton, F. Bellucci, A. Moktefi, P. Chapman, & S. Perez-Kriz (Eds.), Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings (pp. 814-816). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10871 LNAI). Springer Verlag.
Grosholz, Emily Rolfe. / The central role of diagrams in algebraic topology. Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings. editor / Gem Stapleton ; Francesco Bellucci ; Amirouche Moktefi ; Peter Chapman ; Sarah Perez-Kriz. Springer Verlag, 2018. pp. 814-816 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Grosholz, ER 2018, The central role of diagrams in algebraic topology. in G Stapleton, F Bellucci, A Moktefi, P Chapman & S Perez-Kriz (eds), Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10871 LNAI, Springer Verlag, pp. 814-816, 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 , Edinburgh, United Kingdom, 6/18/18.

The central role of diagrams in algebraic topology. / Grosholz, Emily Rolfe.

Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings. ed. / Gem Stapleton; Francesco Bellucci; Amirouche Moktefi; Peter Chapman; Sarah Perez-Kriz. Springer Verlag, 2018. p. 814-816 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10871 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Grosholz ER. The central role of diagrams in algebraic topology. In Stapleton G, Bellucci F, Moktefi A, Chapman P, Perez-Kriz S, editors, Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings. Springer Verlag. 2018. p. 814-816. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).