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Rigidity of a rank $1$ cusp of punctured-surface groups in hyperbolic $4$-space

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We prove that a punctured-torus group of hyperbolic $4$-space which keeps an embedded hyperbolic $2$-plane invariant has a strictly parabolic commutator. More generally, this rigidity persists for a punctured-surface group.

Abstract

We prove that a punctured-torus group of hyperbolic $4$-space which keeps an embedded hyperbolic $2$-plane invariant has a strictly parabolic commutator. More generally, this rigidity persists for a punctured-surface group.

참고문헌 (20)

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