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<p>In this paper, we investigate the MD-homology of definable surface germs for the inner and outer metrics. We completely determine the MD-homology of surfaces for the inner metric and we present a great variety of interesting MD-homology of surfaces for the outer metric, for instance, we determine the MD-homology of some bubbles, snake surfaces, and horns. Furthermore, we explicit the diversity of MD-homology of surfaces for the outer metric in general, showing how difficult the outer classification problem is. On the other hand, we show that, under specific conditions, the weakly outer Lipschitz equivalence completely determines the MD-homology of surfaces for the outer metric, showing that these two subjects are quite related.</p>

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Moderately discontinuous homology of real surfaces

  • 期刊论文

  • 发表日期：

    2025年8月26日

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  • Davi Lopes Medeiros,
  • José Edson Sampaio,
  • Emanoel Souza

摘要

In this paper, we investigate the MD-homology of definable surface germs for the inner and outer metrics. We completely determine the MD-homology of surfaces for the inner metric and we present a great variety of interesting MD-homology of surfaces for the outer metric, for instance, we determine the MD-homology of some bubbles, snake surfaces, and horns. Furthermore, we explicit the diversity of MD-homology of surfaces for the outer metric in general, showing how difficult the outer classification problem is. On the other hand, we show that, under specific conditions, the weakly outer Lipschitz equivalence completely determines the MD-homology of surfaces for the outer metric, showing that these two subjects are quite related.