Some spaces of polynomial knots

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• 作者：Hitesh Raundal ^{hiteshrndl@gmail.com} ; Rama Mishra ; ^{ramamishra64@gmail.com}
• 关键词：14P10 ; 55P15 ; 57M25 ; 57R40 ; 57R52
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：218
• 期：Complete
• 页码：66-92
• 全文大小：753 K
• 卷排序：218

文摘

In this paper we study the topology of three different kinds of spaces associated to polynomial knots of degree at most d  , for d≥2d≥2. We denote these spaces by OdOd, PdPd and QdQd. For d≥3d≥3, we show that the spaces OdOd and PdPd are path connected and the space OdOd has the same homotopy type as S2S2. Considering the space P=⋃b>d≥2OdP=⋃d≥2Od of all polynomial knots with the inductive limit topology, we prove that it too has the same homotopy type as S2S2. We also show that if two polynomial knots are path equivalent in QdQd, then they are topologically equivalent. Furthermore, the number of path components in QdQd are in multiples of eight.