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Name of reference; `K` -> `$K$`; `M` -> `$M$`
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LSpice
LSpice
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Two things I am aware of:

(1) If $K^{c}$ is a finite disjoint union of stably-displaceable sets. Then K is a stable stem. (This is explained in 1.2 in the paper you cited.) And a stable stem is super-heavy. (Theorem 1.8 in the same paper.)

(2) If M is Calabi-Yau or negatively monotone, then Ishikawa proved that the complement of disjoint open balls is super-heavy. (See Theorem 1.1 https://arxiv.org/abs/1507.02760 for the general statement.)

  1. If $K^{c}$ is a finite disjoint union of stably-displaceable sets. Then $K$ is a stable stem. (This is explained in 1.2 in the paper you cited Entov and Polterovich - Rigid subsets of symplectic manifolds.) And a stable stem is super-heavy. (Theorem 1.8 in the same paper.)

  2. If $M$ is Calabi–Yau or negatively monotone, then Ishikawa proved that the complement of disjoint open balls is super-heavy. (See Theorem 1.1 of Spectral invariants of distance functions for the general statement.)

Remark: these two results both support your feeling that there is a relation between $SH^{*}(K^{c})=0$ and $K$ being super-heavy, in a rough sense. (I am not sure what version of symplectic cohomology you used here for $K^{c}$.)

Two things I am aware of:

(1) If $K^{c}$ is a finite disjoint union of stably-displaceable sets. Then K is a stable stem. (This is explained in 1.2 in the paper you cited.) And a stable stem is super-heavy. (Theorem 1.8 in the same paper.)

(2) If M is Calabi-Yau or negatively monotone, then Ishikawa proved that the complement of disjoint open balls is super-heavy. (See Theorem 1.1 https://arxiv.org/abs/1507.02760 for the general statement.)

Remark: these two results both support your feeling that there is a relation between $SH^{*}(K^{c})=0$ and $K$ being super-heavy, in a rough sense. (I am not sure what version of symplectic cohomology you used here for $K^{c}$.)

Two things I am aware of:

  1. If $K^{c}$ is a finite disjoint union of stably-displaceable sets. Then $K$ is a stable stem. (This is explained in 1.2 in the paper you cited Entov and Polterovich - Rigid subsets of symplectic manifolds.) And a stable stem is super-heavy. (Theorem 1.8 in the same paper.)

  2. If $M$ is Calabi–Yau or negatively monotone, then Ishikawa proved that the complement of disjoint open balls is super-heavy. (See Theorem 1.1 of Spectral invariants of distance functions for the general statement.)

Remark: these two results both support your feeling that there is a relation between $SH^{*}(K^{c})=0$ and $K$ being super-heavy, in a rough sense. (I am not sure what version of symplectic cohomology you used here for $K^{c}$.)

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Yuhan
Yuhan
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Two things I am aware of:

(1) If $K^{c}$ is a finite disjoint union of stably-displaceable sets. Then K is a stable stem. (This is explained in 1.2 in the paper you cited.) And a stable stem is super-heavy. (Theorem 1.8 in the same paper.)

(2) If M is Calabi-Yau or negatively monotone, then Ishikawa proved that the complement of disjoint open balls is super-heavy. (See Theorem 1.1 https://arxiv.org/abs/1507.02760 for the general statement.)

Remark: these two results both support your feeling that there is a relation between $SH^{*}(K^{c})=0$ and $K$ being super-heavy, in a rough sense. (I am not sure what version of symplectic cohomology you used here for $K^{c}$.)