Moderately discontinuous homology of real surfaces

Davi Lopes Medeiros ^[1] ; José Edson Sampaio ^[1] ; Emanoel Souza ^[2]
1. [1] Universidade Federal do Ceará
  
  Universidade Federal do Ceará
  
  Brasil
2. [2] Universidade Estadual do Ceará
  
  Universidade Estadual do Ceará
  
  Brasil
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
Idioma: inglés
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Resumen
- 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.