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- W2964215212 abstract "In this paper we study the topology of three different kinds of spaces associated to polynomial knots of degree at most d , for d ≥ 2 . We denote these spaces by O d , P d and Q d . For d ≥ 3 , we show that the spaces O d and P d are path connected and the space O d has the same homotopy type as S 2 . Considering the space P = ⋃ d ≥ 2 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 Q d , then they are topologically equivalent. Furthermore, the number of path components in Q d are in multiples of eight." @default.
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- W2964215212 date "2017-03-01" @default.
- W2964215212 modified "2023-09-29" @default.
- W2964215212 title "Some spaces of polynomial knots" @default.
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- W2964215212 doi "https://doi.org/10.1016/j.topol.2016.12.020" @default.
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