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On the capacity and depth of compact surfaces

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Abstract

K. Borsuk in 1979, at the Topological Conference in Moscow, introduced the concept of capacity and depth of a compactum. In this paper we compute the capacity and depth of compact surfaces. We show that the capacity and depth of every compact orientable surface of genus \(g\ge 0\) is equal to \(g+2\). Also, we prove that the capacity and depth of a compact non-orientable surface of genus \(g>0\) is \([\frac{g}{2}]+2\).

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Correspondence to Behrooz Mashayekhy.

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Communicated by Jim Stasheff.

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Abbasi, M., Mashayekhy, B. On the capacity and depth of compact surfaces. J. Homotopy Relat. Struct. (2020). https://doi.org/10.1007/s40062-020-00254-4

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Keywords

  • Capacity
  • Compact surface
  • Homotopy domination
  • Homotopy type
  • Eilenberg–MacLane space
  • Polyhedron

Mathematics Subject Classification

  • 55P55
  • 55P15
  • 55P20