Singular Homology of Hypergestures

Guerino Mazzola, René Guitart, Jocelyn Ho, Alex Lubet, Maria Mannone, Matt Rahaim, Florian Thalmann

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this chapter we interpret the basic cubic chain spaces of singular homology in terms of hypergestures in a topological space over a series of copies of the arrow digraph ò. This interpretation allows for a generalized homological setup. The generalization is (1) to topological categories instead of topological spaces, and (2) to any sequence of digraph pΓnqnPZ instead of the constant series of Ò. We then define the corresponding chain complexes, and prove the core boundary operator equation B2 “ 0, enabling the associated homology modules over a commutative ring R. We discuss some geometric examples and a musical one, interpreting contrapuntal rules in terms of singular homology.

Original languageEnglish (US)
Title of host publicationComputational Music Science
PublisherSpringer Nature
Pages965-972
Number of pages8
DOIs
StatePublished - 2017

Publication series

NameComputational Music Science
ISSN (Print)1868-0305
ISSN (Electronic)1868-0313

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing AG, part of Springer Nature.

Fingerprint

Dive into the research topics of 'Singular Homology of Hypergestures'. Together they form a unique fingerprint.

Cite this