Published on:

8 January 2024

Primary Category:

Geometric Topology

Paper Authors:

Boris N. Apanasov

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Introduce fractal Sierpinski carpet in nilpotent geometry at infinity

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Show this yields non-rigid hyperbolic groups and spaces

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Two cases considered: whole sphere at infinity is the limit set, or just components of it

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Non-rigidity tied to non-ergodic group dynamics on the limit set

Non-rigidity of deformations of locally symmetric spaces

This paper constructs examples of discrete hyperbolic groups acting on rank one symmetric spaces over R, C, H, or O whose deformations are non-rigid. This is done by introducing a Sierpinski carpet fractal set and associated stretchings in the nilpotent geometry at infinity. The constructed groups have non-trivial deformations induced by equivariant homeomorphisms, related to non-ergodic group action on the limit set.

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