Five Dimensional Knot Theory

by

Samuel J. Lomonaco, Jr. (*) 

Published in "Low Dimensional Topology," Contemporary Mathematics Series of the American Mathematics Society, Providence, Rhode Island, Vol. 20 (1984), pp 249 - 270.

ABSTRACT.

This paper outlines in an informal and intuitive fashion a method for computing the second homotopy group   p2(X)  (as a left  Zp1(X) -module) of the complement  X = S5 - kM3  of a smooth 3-knot  (S5, kM3). By a smooth 3-knot  (S5, kM3)  is meant a smooth imbedding of a closed 3-manifold  M3  in the 5-sphere  S5 . An example of the calculation is given.

The methods of this paper may also be used to compute the Rohlin invariant of 3-manifolds from their imbeddings in S5 .


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(*) Partially supported by the L-O-O-P Fund.