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Adamaszek and Adams have studied the Vietoris-Rips complexes of $S^1$ with different radii, and proved that the resulting Vietoris-Rips complex can be of arbitrary dimension. A number of examples with finite points are treated on the way (with, with the same result). See https://msp.org/pjm/2017/290-1/p01.xhtml as well as subsequent papers.

Adamaszek and Adams have studied the Vietoris-Rips complexes of $S^1$ with different radii, and proved that the resulting Vietoris-Rips complex can be of arbitrary dimension. A number of examples with finite points are treated on the way (with the same result). See https://msp.org/pjm/2017/290-1/p01.xhtml as well as subsequent papers.

Adamaszek and Adams have studied the Vietoris-Rips complexes of $S^1$ with different radii, and proved that the resulting Vietoris-Rips complex can be of arbitrary dimension. A number of examples with finite points are treated on the way, with the same result. See https://msp.org/pjm/2017/290-1/p01.xhtml as well as subsequent papers.

Source Link
APR
APR
  • 352
  • 2
  • 11

Adamaszek and Adams have studied the Vietoris-Rips complexes of $S^1$ with different radii, and proved that the resulting Vietoris-Rips complex can be of arbitrary dimension. A number of examples with finite points are treated on the way (with the same result). See https://msp.org/pjm/2017/290-1/p01.xhtml as well as subsequent papers.