$\textbf {Z}_{(2)}$-knot cobordism in codimension two, and involutions on homotopy spheres
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- by Chao Chu Liang PDF
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Abstract:
Let ${Z_{(2)}}$ denote the ring of rational 2-adic integers. In this paper, we consider the group ${\Psi _k}$ of ${Z_{(2)}}$-cobordism classes of ${Z_{(2)}} - \operatorname {knot} (\Sigma ^{k + 2}, {K^k})$, where $\Sigma$ is a 1-connected ${Z_{(2)}}$-sphere ${Z_{(2)}}$-cobordant to ${S^{k + 2}}$, and K is a 1-connected ${Z_{(2)}}$-sphere embedded in $\Sigma$ with trivial normal bundle. For $n \geqslant 3$, we will prove that ${\Psi _{2n}} = 0$ and ${\Psi _{2n - 1}} = {C_\varepsilon }({Z_{(2)}})$, $\varepsilon = {( - 1)^n}$. Also, we will show that the group $\Theta _{4m - 1}^{4m + 1}$ of L-equivalence classes of differentiable involutions on $(4m + 1)$-homotopy spheres with codimension two fixed point sets defined by Bredon contains infinitely many copies of Z.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 256 (1979), 89-97
- MSC: Primary 57R85; Secondary 55M35, 57Q45
- DOI: https://doi.org/10.1090/S0002-9947-1979-0546908-1
- MathSciNet review: 546908