Smooth free involution of $H{\Bbb C}P^3$ and Smith conjecture for imbeddings of $S^3$ in $S^6$

Details Smooth free involution of $H{\Bbb C}P^3$ and Smith conjecture for imbeddings of $S^3$ in $S^6$ Smooth free involution of $H{\Bbb C}P^3$ and Smith conjecture for imbeddings of $S^3$ in $S^6$

2002-11-09

arxiv.org/abs/math/0211153v3

Math. Ann. 339 (2007), 879-889.

Mathematics

Algebraic Topology

10 pages, final version

Scientific paper

10.1007/s00208-007-0134-y

This paper establishes an equivalence between existence of free involutions on $H{\Bbb C}P^3$ and existence of involutions on $S^6$ with fixed point set an imbedded $S^3$, then a family of counterexamples of the Smith conjecture for imbeddings of $S^3$ in $S^6$ are given by known result on $H{\Bbb C}P^3$. In addition, this paper also shows that every smooth homotopy complex projective 3-space admits no orientation preserving smooth free involution, which answers an open problem [Pe]. Moreover, the study of existence problem for smooth orientation preserving involutions on $H{\Bbb C}P^3$ is completed.

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