کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4665423 | 1633814 | 2015 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Counterexamples to Kauffman's conjectures on slice knots
ترجمه فارسی عنوان
نمونه هایی از قضیه کافمن در گره های برش
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
In the late 1960s Jerome Levine classified the odd high-dimensional knot concordance groups in terms of a linking matrix associated to an arbitrary bounding manifold for the knot. His proof fails for classical knots in S3. Yet this philosophy has remained the only known strategy for understanding the classical knot concordance group. We show that this strategy is fundamentally flawed. Specifically, in 1982, in support of Levine's philosophy, Louis Kauffman conjectured that if a knot in S3 is a slice knot then on any Seifert surface for that knot there exists a homologically essential simple closed curve of self-linking zero which is itself a slice knot, or at least has Arf invariant zero. Since that time, considerable evidence has been amassed in support of this conjecture. In particular, many invariants that obstruct a knot from being a slice knot have been explicitly expressed in terms of invariants of such curves on its Seifert surface. We give counterexamples to Kauffman's conjecture, that is, we exhibit (smoothly) slice knots that admit (unique minimal genus) Seifert surfaces on which every homologically essential simple closed curve of self-linking zero has non-zero Arf invariant and non-zero signatures.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 274, 9 April 2015, Pages 263-284
Journal: Advances in Mathematics - Volume 274, 9 April 2015, Pages 263-284
نویسندگان
Tim D. Cochran, Christopher William Davis,