Parity biquandle invariants of virtual knots

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• 作者：Aaron Kaestner^a ; ^{amkaestner@northpark.edu" class="auth_mail" title="E-mail the corresponding author} ; Sam Nelson^b ; ¹ ; ^{sam.nelson@cmc.edu" class="auth_mail" title="E-mail the corresponding author} ; Leo Selker^b ; ^{lselker13@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：57M27 ; 57M25
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：209
• 期：Complete
• 页码：207-219
• 全文大小：399 K

文摘

We define counting and cocycle enhancement invariants of virtual knots using parity biquandles. The cocycle invariants are determined by pairs consisting of a biquandle 2-cocycle d="mmlsi1" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864116301286&_mathId=si1.gif&_user=111111111&_pii=S0166864116301286&_rdoc=1&_issn=01668641&md5=f39719e8e08e242b01874818d816db0a" title="Click to view the MathML source">ϕ⁰dden">de">${\varphi }^0$ and a map d="mmlsi2" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864116301286&_mathId=si2.gif&_user=111111111&_pii=S0166864116301286&_rdoc=1&_issn=01668641&md5=537d32b62473e2d004beb99376af49f9" title="Click to view the MathML source">ϕ¹dden">de">${\varphi }^1$ with certain compatibility conditions leading to one-variable or two-variable polynomial invariants of virtual knots. We provide examples to show that the parity cocycle invariants can distinguish virtual knots which are not distinguished by the corresponding non-parity invariants.