On the Residual Finiteness Growths of Particular Hyperbolic Manifold\n Groups

2014/12/21 by Priyam Patel, Patel, Priyam
Mathematics · #20E26 #20F65 #57M10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1412.6835

openalex publication_date 2014/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a quantification of residual finiteness for the fundamental groups of\nhyperbolic manifolds that admit a totally geodesic immersion to a compact,\nright-angled Coxeter orbifold of dimension 3 or 4. Specifically, we give\nexplicit upper bounds on residual finiteness that are linear in terms of\ngeodesic length. We then extend the linear upper bounds to hyperbolic manifolds\nwith a finite cover that admits such an immersion. Since the quantifications\nare given in terms of geodesic length, we define the geodesic residual\nfiniteness growth and show that this growth is equivalent to the usual residual\nfiniteness growth defined in terms of word length. This equivalence implies\nthat our results recover the quantification of residual finiteness from\n citeBHP for hyperbolic manifolds that virtually immerse into a compact\nreflection orbifold.\n

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