Simply connected 3-manifolds with a dense set of ends of specified genusGarity, Dennis (Avtor) Repovš, Dušan (Avtor) 3-manifold setwild Cantor setlocal genusdefining sequenceexhaustionendWe 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.20172019-09-04 15:08:05Članek v reviji109515UDK: 515.124ISSN pri članku: 1660-5446DOI: http://dx.doi.org/10.1007/s00009-017-0907-9COBISS_ID: 18016345OceCobissID: 13561433sl