Topological Invariants in Engineering Sciences and Quantum Field Theories

Philippe Durand ()
Additional contact information
Philippe Durand: Conservatoire National des Arts et Métiers, Département Mathématiques-Statistiques

Chapter Chapter 3 in Transactions on Engineering Technologies, 2019, pp 29-40 from Springer

Abstract: Abstract The notion of topological invariants is very old. Since long used in pure mathematics, it is now widely used in engineering science, applied mathematics and theoretical physics. We propose here revisiting this notion and giving examples that have advanced the engineering sciences but also mathematical physics. Invariants of a topological nature were discovered from Euler’s work on graphs, and then extended to topological manifolds of all sizes by H. Poincaré, who is at the origin of the algebraic topology at the beginning of the twentieth century. Finally M. Atiyah more recently demonstrates the theorem of the index that E. Witten will operate in physics.

Keywords: Invariants; Graph; Kron method; Moduli spaces; Index theorem; Mathematical physics (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-32-9531-5_3

Ordering information: This item can be ordered from
http://www.springer.com/9789813295315

DOI: 10.1007/978-981-32-9531-5_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().