The mathematics of M-theory. (English) Zbl 1023.81037
Casacuberta, Carles (ed.) et al., 3rd European congress of mathematics (ECM), Barcelona, Spain, July 10-14, 2000. Volume I. Basel: Birkhäuser. Prog. Math. 201, 1-19 (2001).
Summary: String theory, on its modern incarnation M-theory, gives a huge generalization of classical geometry. Here the author indicates how it can be considered as a two-parameter deformation, where one parameter controls the generalization from points to loops, and the other parameter controls the sum over topologies of Riemann surfaces. The final mathematical formulation of M-theory will have to make contact with the theory of vector bundles, \(K\)-theory and noncommutative geometry.
For the entire collection see [Zbl 0972.00031].
For the entire collection see [Zbl 0972.00031].
MSC:
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
81T75 | Noncommutative geometry methods in quantum field theory |
81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |
19M05 | Miscellaneous applications of \(K\)-theory |
58B34 | Noncommutative geometry (à la Connes) |
53D45 | Gromov-Witten invariants, quantum cohomology, Frobenius manifolds |