proposition 24.34 Capacities exist if and only if non-squeezing holds

Rests on

• depends_on definition 24.33 Symplectic capacity ¶
  • depends_on definition 24.28 Ball and cylinder ¶
    • depends_on definition 24.17 Symplectomorphism ¶
      • depends_on definition A.70 Pullback ¶
        • depends_on definition 7.97 Partial derivative; gradient ¶
        • depends_on definition 13.83 Covector ¶
        • depends_on definition 13.98 $k$-form ¶
      • depends_on definition 24.8 Symplectic manifold ¶
        • depends_on definition 13.105 Closed form ¶
        • depends_on definition 13.98 $k$-form ¶ ↺
        • depends_on definition 24.2 Symplectic vector space ¶
    • depends_on remark 24.27 Fixing a scale, so that a ``ball'' means something ¶
      • depends_on equation 22.56 eq:ham-symplectic-matrix ¶
      • depends_on remark 24.11 The SI dimension of every object in this chapter ¶
        • depends_on proposition 24.10 The canonical form is symplectic and intrinsic ¶
        • depends_on remark 22.5 Units ¶
  • depends_on remark 24.27 Fixing a scale, so that a ``ball'' means something ¶ ↺
• depends_on theorem 24.31 Gromov's non-squeezing theorem ¶
  • depends_on definition 24.28 Ball and cylinder ¶ ↺
  • depends_on proposition 24.30 Linear non-squeezing ¶
    • depends_on definition 24.28 Ball and cylinder ¶ ↺
    • depends_on definition 24.4 Symplectic group ¶
      • depends_on definition 5.135 The symplectic group ¶
        • depends_on definition 5.113 Non-degenerate form ¶
        • depends_on equation 5.138 eq:lin-bilinear-expansion ¶
        • depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
      • depends_on proposition 24.3 Even dimension and the canonical basis ¶
        • depends_on definition 24.2 Symplectic vector space ¶ ↺
        • depends_on equation 22.56 eq:ham-symplectic-matrix ¶ ↺
        • depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶ ↺
        • proves proof ch:07-symplectic-geometry@proof-1 ¶
    • depends_on equation 24.19 eq:sym-omega-euclid ¶
    • proves proof ch:07-symplectic-geometry@proof-11 ¶
• proves proof ch:07-symplectic-geometry@proof-12 ¶

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