Quantifying separability in limit groups via representations

• Keino Brown ^[1] ; Olga Kharlampovich ^[2]
  1. [1] City College

     City College

     Estados Unidos

     
  2. [2] CUNY, Graduate Center and Hunter College, New York, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 1, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-024-01008-3
• Enlaces
  • Texto completo
• Resumen

  • We show that for any finitely generated subgroup H of a limit group L there exists a finite-index subgroup K containing H, such that K is a subgroup of a group obtained from H by a series of extensions of centralizers and free products with Z. If H is non-abelian, the K is fully residually H. We also show that for any finitely generated subgroup of a limit group, there is a finite-dimensional representation of the limit group which separates the subgroup in the induced Zariski topology.rollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a limit group. This generalizes the results in (Louder et al. in Sel Math New Ser 23:2019–2027, 2017). Another corollary is that a hyperbolic limit group satisfies the Geometric Hanna Neumann conjecture.

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