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33 relations: André Lichnerowicz, Arithmetic genus, Armand Borel, Atiyah–Singer index theorem, Bernoulli number, Closed manifold, Dirac operator, Eisenstein series, Elementary symmetric polynomial, Formal power series, Friedrich Hirzebruch, Fundamental class, H. Blaine Lawson, Hirzebruch signature theorem, Hirzebruch–Riemann–Roch theorem, John Milnor, List of cohomology theories, Mathematics, Mikhail Leonidovich Gromov, Modular form, Nigel Hitchin, Piecewise linear manifold, Pontryagin class, Rational number, Ring (mathematics), Ring homomorphism, Rokhlin's theorem, Sequence, Signature (topology), Smooth structure, Spin structure, Weierstrass functions, Weitzenböck identity.
André Lichnerowicz
André Lichnerowicz (January 21, 1915 – December 11, 1998) was a noted French differential geometer and mathematical physicist of Polish descent.
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Arithmetic genus
In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface.
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Armand Borel
Armand Borel (21 May 1923 – 11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993.
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Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by, states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).
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Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
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Closed manifold
In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.
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Dirac operator
In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian.
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Eisenstein series
Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written down directly.
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Elementary symmetric polynomial
In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed as a polynomial in elementary symmetric polynomials.
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Formal power series
In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.
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Friedrich Hirzebruch
Friedrich Ernst Peter Hirzebruch ForMemRS (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation.
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Fundamental class
In mathematics, the fundamental class is a homology class associated to an oriented manifold M of dimension n, which corresponds to the generator of the homology group H_n(M;\mathbf)\cong\mathbf.
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H. Blaine Lawson
Herbert Blaine Lawson, Jr. is a mathematician best known for his work in minimal surfaces, calibrated geometry, and algebraic cycles.
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Hirzebruch signature theorem
In differential topology, an area of mathematics, the Hirzebruch signature theorem (sometimes called the Hirzebruch index theorem) is Friedrich Hirzebruch's 1954 result expressing the signature of a smooth compact oriented manifold by a linear combination of Pontryagin numbers called the L-genus.
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Hirzebruch–Riemann–Roch theorem
In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result contributing to the Riemann–Roch problem for complex algebraic varieties of all dimensions.
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John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, K-theory and dynamical systems.
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List of cohomology theories
This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Mikhail Leonidovich Gromov
Mikhail Leonidovich Gromov (also Mikhael Gromov, Michael Gromov or Mischa Gromov; Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French-Russian mathematician known for work in geometry, analysis and group theory.
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Modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.
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Nigel Hitchin
Nigel James Hitchin FRS (born 2 August 1946) a British mathematician working in the fields of differential geometry, algebraic geometry, and mathematical physics.
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Piecewise linear manifold
In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it.
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Pontryagin class
In mathematics, the Pontryagin classes, named for Lev Pontryagin, are certain characteristic classes.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
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Ring homomorphism
In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.
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Rokhlin's theorem
In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, compact 4-manifold M has a spin structure (or, equivalently, the second Stiefel–Whitney class w2(M) vanishes), then the signature of its intersection form, a quadratic form on the second cohomology group H2(M), is divisible by 16.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Signature (topology)
In the mathematical field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension d.
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Smooth structure
In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function.
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Spin structure
In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry.
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Weierstrass functions
In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function.
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Weitzenböck identity
In mathematics, in particular in differential geometry, mathematical physics, and representation theory a Weitzenböck identity, named after Roland Weitzenböck, expresses a relationship between two second-order elliptic operators on a manifold with the same leading symbol.
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Redirects here:
A genus, A hat genus, A-genus, A-hat genus, A-hat polynomial, Elliptic genera, Elliptic genus, Equivariant signature theorem, G-signature theorem, Hirzebruch L-polynomial, Hirzebruch polynomial, L genus, L-genus, Witten genus, Â genus, Â-genus.
References
[1] https://en.wikipedia.org/wiki/Genus_of_a_multiplicative_sequence
