topological genus
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Topological order — In physics, topological order is a new kind of order (a newkind of organization of particles) in a quantum state that is beyond theLandau symmetry breaking description. It cannot be described by local order parameters and long rangecorrelations.… … Wikipedia
Genus (mathematics) — In mathematics, genus has a few different, but closely related, meanings:TopologyOrientable surfaceThe genus of a connected, orientable surface is an integer representing the maximum number of cuttings along closed simple curves without rendering … Wikipedia
Topological graph theory — In mathematics topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, and graphs as topological spaces. [J.L. Gross and T.W. Tucker, Topological graph theory, Wiley Interscience, 1987] Embedding a… … Wikipedia
Topological modular forms — In mathematics, the spectrum of topological modular forms (also known as tmf ) describes a generalized cohomology theory whose coefficient ring is similar to the graded ring of holomorphic modular forms with integral cusp expansions. These rings… … Wikipedia
Genus of a multiplicative sequence — In mathematics, the genus of a multiplicative sequence is a ring homomorphism, from the cobordism ring of smooth oriented compact manifolds to another ring, usually the ring of rational numbers.DefinitionA genus phi; assigns a number phi;( X ) to … Wikipedia
Slice genus — In mathematics, the slice genus of a smooth knot K in S3 (sometimes called its Murasugi genus or 4 ball genus ) is the least integer g such that K is the boundary of a connected, orientable 2 manifold S of genus g embedded in the 4 ball D4… … Wikipedia
Arithmetic genus — In mathematics, the arithmetic genus of an algebraic variety is one of some possible generalizations of the genus of an algebraic curve or Riemann surface.The arithmetic genus of a complex manifold of dimension n can be defined as a combination… … Wikipedia
Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… … Wikipedia
Mathematics and Physical Sciences — ▪ 2003 Introduction Mathematics Mathematics in 2002 was marked by two discoveries in number theory. The first may have practical implications; the second satisfied a 150 year old curiosity. Computer scientist Manindra Agrawal of the… … Universalium
Riemann–Roch theorem — In mathematics, specifically in complex analysis and algebraic geometry, the Riemann–Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates… … Wikipedia
Gustav Roch — (december 9 1839 november 21 1866) was a German mathematician who made significant contributions to the theory of Riemann surfaces in a career that was prematurely curtailed at the age of 26.BiographyBorn in Leipzig, Roch attended the Polytechnic … Wikipedia
