Crosscap numbers and the Jones polynomial

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• 作者：Efstratia Kalfagianni^a ; ^{kalfagia@math.msu.edu" class="auth_mail" title="E-mail the corresponding author} ; Christine Ruey Shan Lee^b ; ¹ ; ^{clee@math.utexas.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Alternating knot ; Jones polynomial ; Crosscap number (non-orientable genus) ; Normal surfaces ; Spanning surfaces ; Augmented links
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：2 January 2016
• 年：2016
• 卷：286
• 期：Complete
• 页码：308-337
• 全文大小：932 K

文摘

We give sharp two-sided linear bounds of the crosscap number (non-orientable genus) of alternating links in terms of their Jones polynomial. Our estimates are often exact and we use them to calculate the crosscap numbers for several infinite families of alternating links and for several alternating knots with up to twelve crossings. We also discuss generalizations of our results for classes of non-alternating links.