کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6424707 1344295 2013 5 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On Krebesʼs tangle
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
On Krebesʼs tangle
چکیده انگلیسی

A genus-1 tangle G is an arc properly embedded in a standardly embedded solid torus S in the 3-sphere. We say that a genus-1 tangle embeds in a knot K⊆S3 if the tangle can be completed by adding an arc exterior to the solid torus to form the knot K. We call K a closure of G. An obstruction to embedding a genus-1 tangle G in a knot is given by torsion in the homology of branched covers of S branched over G. We examine a particular example A of a genus-1 tangle, given by Krebes, and consider its two double-branched covers. Using this homological obstruction, we show that any closure of A obtained via an arc which passes through the hole of S an odd number of times must have determinant divisible by three. A resulting corollary is that if A embeds in the unknot, then the arc which completes A to the unknot must pass through the hole of S an even number of times.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 160, Issue 12, 1 August 2013, Pages 1379-1383
نویسندگان
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