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About: Systolic freedom

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In differential geometry, systolic freedom refers to the fact that closed Riemannian manifolds may have arbitrarily small volume regardless of their systolic invariants.That is, systolic invariants or products of systolic invariants do not in general provide universal (i.e. curvature-free) lower bounds for the total volume of a closed Riemannian manifold. Systolic freedom has applications in quantum error correction. survey the main results on systolic freedom.

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  • In differential geometry, systolic freedom refers to the fact that closed Riemannian manifolds may have arbitrarily small volume regardless of their systolic invariants.That is, systolic invariants or products of systolic invariants do not in general provide universal (i.e. curvature-free) lower bounds for the total volume of a closed Riemannian manifold. Systolic freedom was first detected by Mikhail Gromov in an I.H.É.S. preprint in 1992 (which eventually appeared as ), and was further developed by Mikhail Katz, Michael Freedman and others. Gromov's observation was elaborated on by Marcel Berger. One of the first publications to study systolic freedom in detail is by . Systolic freedom has applications in quantum error correction. survey the main results on systolic freedom. (en)
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  • 19942528 (xsd:integer)
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  • 3591 (xsd:nonNegativeInteger)
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  • 1087471090 (xsd:integer)
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  • Marcel Berger (en)
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  • Marcel (en)
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  • Berger (en)
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  • 1993 (xsd:integer)
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  • In differential geometry, systolic freedom refers to the fact that closed Riemannian manifolds may have arbitrarily small volume regardless of their systolic invariants.That is, systolic invariants or products of systolic invariants do not in general provide universal (i.e. curvature-free) lower bounds for the total volume of a closed Riemannian manifold. Systolic freedom has applications in quantum error correction. survey the main results on systolic freedom. (en)
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  • Systolic freedom (en)
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