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Equivariant intersection forms, knots in $ S\sp 4$, and rotations in $ 2$-spheres


Author: Steven P. Plotnick
Journal: Trans. Amer. Math. Soc. 296 (1986), 543-575
MSC: Primary 57Q45; Secondary 57M10, 57M99, 57R50
DOI: https://doi.org/10.1090/S0002-9947-1986-0846597-6
MathSciNet review: 846597
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Abstract: We consider the problem of distinguishing the homotopy types of certain pairs of nonsimply-connected four-manifolds, which have identical three-skeleta and intersection pairings, by the equivariant isometry classes of the intersection pairings on their universal covers. As applications of our calculations, we: (i) construct distinct homology four-spheres with the same three-skeleta, (ii) generalize a theorem of Gordon to show that any nontrivial fibered knot in $ {S^4}$ with odd order monodromy is not determined by its complement, and (iii) give a more constructive proof of a theorem of Hendriks concerning rotations in two-spheres embedded in threemanifolds.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0846597-6
Article copyright: © Copyright 1986 American Mathematical Society

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