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Some spaces of polynomial knots
Raundal, Hitesh...

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Some spaces of polynomial knots by Raundal, Hitesh ( Author )
Lemonjar Open Access
Australian National University
08-08-2023
In this paper we study the topology of three different kinds of spaces associated to polynomial knots of degree at most $d$, for $d\geq2$. We denote these spaces by $\mathcal{O}_d$, $\mathcal{P}_d$ and $\mathcal{Q}_d$. For $d\geq3$, we show that the spaces $\mathcal{O}_d$ and $\mathcal{P}_d$ are path connected and the space $\mathcal{O}_d$ has the same homotopy type as $S^2$. Considering the space $\mathcal{P}=\bigcup_{d\geq2}\mathcal{O}_d$ of all polynomial knots with the inductive limit topology, we prove that it too has the same homotopy type as $S^2$. We also show that if two polynomial knots are path equivalent in $\mathcal{Q}_d$, then they are topologically equivalent. Furthermore, the number of path components in $\mathcal{Q}_d$ are in multiples of eight.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1603.09110
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