The geometry and fundamental groups of solenoid complements

Conner, Gregory R. (avtor), Meilstrup, Mark H. (avtor), Repovš, Dušan (avtor)

A solenoid is an inverse limit of circles. When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse limits) have different fundamental groups. Embeddings of the same solenoid can give different groups; in particular, the nicest embeddings are unknotted at each level, and give an Abelian fundamental group, while other embeddings have non-Abelian groups. We show using geometry that every solenoid has uncountably many embeddings with nonhomeomorphic complements.

• Jezik: Angleški jezik
• Ključne besede: solenoid, 3-manifold, inverse limit, embedding, fundamental group, knot complement, braid, Jaco-Shalen-Johannson decomposition, Mostow-Prasad rigidity
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2015
• Št. strani: 20 str.
• Številčenje: Vol. 24, iss. 14
• PID: 20.500.12556/RUL-111223
• UDK: 515.162
• ISSN pri članku: 0218-2165
• DOI: 10.1142/S0218216515500698
• COBISS.SI-ID: 17540697
• Datum objave v RUL: 26.09.2019

Gradivo je del revije

• Naslov: Journal of knot theory and its ramifications
• Skrajšan naslov: J. knot theory ramif.
• Založnik: World Scientific
• ISSN: 0218-2165
• COBISS.SI-ID: 3996249