منابع مشابه
Constructive invariant theory for tori
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متن کاملConstructive Invariant Theory
Invariant theory has been a major subject of research in the 19th century. One of the highlights was Gordan’s famous theorem from 1868 showing that the invariants and covariants of binary forms have a finite basis. His method was constructive and led to explicit degree bounds for a system of generators (Jordan 1876/79). In 1890, Hilbert presented a very general finiteness result using completel...
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Many of the central equations of mathematical physics, the nonlinear wave equation, the nonlinear Schrödinger equation, the Euler equations for free surfaces, can be posed as Hamiltonian systems with infinitely many degrees of freedom. In a neighborhood of an equilibrium, the linearized equations are those of a harmonic oscillator and thus solutions exhibit periodic and quasi-periodic motion. T...
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Let X be a Z[Z]–homology S1 × S3, that is, a smooth closed oriented 4manifold such that H∗(X;Z) = H∗(S 1 × S3;Z) and H∗(X̃;Z) = H∗(S 3;Z), where X̃ is the universal abelian cover of X. Denote by M∗(X) the moduli space of irreducible ASD connections on a trivial SU(2)-bundle over X. The virtual dimension of M∗(X) is −3(1 − b1 + b + 2 )(X) = 0. In fact, M ∗(X) coincides with the moduli space of irr...
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This is the third in our series of papers relating gauge theoretic invariants of certain 4–manifolds with invariants of 3–manifolds derived from Rohlin’s theorem. Such relations are well-known in dimension three, starting with Casson’s integral lift of the Rohlin invariant of a homology sphere. We consider two invariants of a spin 4–manifold that has the integral homology of a 4–torus. The firs...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1993
ISSN: 0373-0956
DOI: 10.5802/aif.1364