On hyperbolic cobweb manifolds

2017/01/24 by Emil Molnár, Molnár, Emil, Jenő Szirmai +1
Chemistry · Computer Science · Mathematics · #52C17 #57M07 #57M60 #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Molecular spectroscopy and chirality #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1701.06757

openalex publication_date 2017/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A compact hyperbolic "cobweb" manifold (hyperbolic space form) of symbol Cw(6,6,6) will be constructed in Fig.1,4,5 as a representant of a presumably infinite series Cw(2p,2p,2p) (3 ≤ p ∈ \bN natural numbers). This is a by-product of our investigations \citeMSz16. In that work dense ball packings and coverings of hyperbolic space \HYP have been constructed on the base of complete hyperbolic Coxeter orthoschemes O=W_uvw and its extended reflection groups \bG (see diagram in Fig.~3. and picture of fundamental domain in Fig.~2). Now u=v=w=6 (=2p). Thus the maximal ball contained in Cw(6,6,6), moreover its minimal covering bal l (so diameter) can also be determined. The algorithmic procedure provides us with the proof of our statements.

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