期刊
MEDITERRANEAN JOURNAL OF MATHEMATICS
卷 14, 期 3, 页码 -出版社
SPRINGER BASEL AG
DOI: 10.1007/s00009-017-0907-9
关键词
3-manifold set; wild Cantor set; local genus; defining sequence; exhaustion; end
资金
- NSF [DMS 0139678]
- SRA [P1-0292, J1-6721, BI-US/15-16-029]
We show that for every sequence (n(i)), where each n(i) is either an integer greater than 1 or is infinity, 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.
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