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Inequivalent Cantor sets in ▫$R^3$▫ whose complements have the same fundamental groupGarity, Dennis, 1950- ; Repovš, Dušan, 1954-For each Cantor set ▫$C$▫ in ▫$R^3$▫, all points of which have bounded local genus, we show that there are infinitely many inequivalent Cantor sets in ▫$R^3$▫ with the complement having the same ... fundamental group as the complement of T$C$T. This answers a question from "Open Problems in Topology" and has as anapplication a simple construction of nonhomeomorphic open -manifolds with the same fundamental group. The main techniques used are analysis of local genus of points of Cantor sets, a construction for producing rigid Cantor sets with simply connected complement, and manifold decomposition theory. The results presented give an argument that for certain groups ▫$G$▫, there are uncountably many nonhomeomorphic open 3-manifolds with fundamental group ▫$G$▫.Source: Proceedings of the American Mathematical Society. - ISSN 0002-9939 (Vol. 141, no. 8, 2013, str. 2901-2911)Type of material - article, component partPublish date - 2013Language - englishCOBISS.SI-ID - 16636505
Author
Garity, Dennis, 1950- |
Repovš, Dušan, 1954-
Topics
matematika |
topologija |
Cantorjeva množica |
togost |
lokalni rod |
definicijsko zaporedje |
konec |
odprta 3-mnogoterost |
fundamentalna grupa |
mathematics |
topology |
Cantor set |
rigidity |
local genus |
defining sequence |
end |
open 3-manifold |
fundamental group
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Garity, Dennis, 1950- | ![]() |
Repovš, Dušan, 1954- | 07083 |
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