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The homological mirror symmetry conjecture of Maxim Kontsevich states that the derived category of coherent sheaves on one Calabi–Yau manifold is equivalent in a certain sense to the Fukaya category of its mirror. [54] This equivalence provides a precise mathematical formulation of mirror symmetry in topological string theory.
The topological insulators and superconductors are classified here in ten symmetry classes (A,AII,AI,BDI,D,DIII,AII,CII,C,CI) named after Altland–Zirnbauer classification, defined here by the properties of the system with respect to three operators: the time-reversal operator , charge conjugation and chiral symmetry . The symmetry classes are ...
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property .
In 1988 Ford Motor Company sold 80% of Ford-New Holland Inc. to Fiat, and in 1991 Fiat acquired the remaining 20%, with the agreement to stop using the Ford brand by 2000. By 1999, Fiat had discontinued the use of both its own and the Ford name, and united them both under the New Holland brand.
This is a list of useful examples in general topology, a field of mathematics. Alexandrov topology; Cantor space; Co-kappa topology Cocountable topology; Cofinite topology; Compact-open topology; Compactification; Discrete topology; Double-pointed cofinite topology; Extended real number line; Finite topological space; Hawaiian earring; Hilbert cube
A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces , and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology.
That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry ...
These two conjectures encode the predictions of mirror symmetry in different ways: homological mirror symmetry in an algebraic way, and the SYZ conjecture in a geometric way. [ 6 ] There should be a relationship between these three interpretations of mirror symmetry, but it is not yet known whether they should be equivalent or one proposal is ...