Simply connected 3-manifolds with a dense set of ends of specified genus

Garity, Dennis (avtor), Repovš, Dušan (avtor)

We show that for every sequence ▫$(n_i)$▫, where each ▫$n_i$▫ is either an integer greater than 1 or is ▫$\infty$▫, there exists a simply connected open 3-manifold ▫$M$▫ with a countable dense set of ends ▫$\{e_i\}$▫ so that, for every ▫$i$▫, the genus of end ▫$e_i$▫ is equal to ▫$n_i$▫. In addition, the genus of the ends not in the dense set is shown to be less than or equal to 2. These simply connected 3-manifolds are constructed as the complements of certain Cantor sets in ▫$S^3$▫. The methods used require careful analysis of the genera of ends and new techniques for dealing with infinite genus.

• Jezik: Angleški jezik
• Ključne besede: 3-manifold set, wild Cantor set, local genus, defining sequence, exhaustion, end
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2017
• Št. strani: 12 str.
• Številčenje: art. 109, iss. 3
• PID: 20.500.12556/RUL-109515
• UDK: 515.124
• ISSN pri članku: 1660-5446
• DOI: http://dx.doi.org/10.1007/s00009-017-0907-9
• COBISS.SI-ID: 18016345
• Datum objave v RUL: 04.09.2019

Gradivo je del revije

• Naslov: Mediterranean journal of mathematics
• Skrajšan naslov: Mediterr. j. math.
• Založnik: Springer Nature, Birkhäuser
• ISSN: 1660-5446
• COBISS.SI-ID: 13561433