Topological Invariants in Engineering Sciences and Quantum Field Theories

Philippe Durand (1)

1 M2N - Modélisation mathématique et numérique

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.

Domaines: Mathématiques [math]; Physique [physics]; Sciences de l'ingénieur [physics]

Philippe Durand. Topological Invariants in Engineering Sciences and Quantum Field Theories. Transactions on Engineering Technologies, Springer Singapore, pp.29-40, 2019, 978-981-32-9531-5. ⟨10.1007/978-981-32-9531-5_3⟩. ⟨hal-04101509⟩