How highly connected can an orbifold be?

Christian Lange ^[1] ; Marco Radeschi ^[2]
1. [1] Ludwig Maximilian University of Munich
  
  Ludwig Maximilian University of Munich
  
  Kreisfreie Stadt München, Alemania
2. [2] University of Notre Dame
  
  University of Notre Dame
  
  Township of Portage, Estados Unidos
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 6, 2023, págs. 2171-2186
Idioma: inglés
DOI: 10.4171/RMI/1375
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Resumen
- On the one hand, we provide the first examples of arbitrarily highly connected (compact) bad orbifolds. On the other hand, we show that n-connected n-orbifolds are manifolds. The latter improves the best previously known bound of Lytchak by roughly a factor of 2. For compact orbifolds and in most dimensions, we prove slightly better bounds. We obtain sharp results up to dimension 5.