The second homotopy group of a spun knot
Samuel J. Lomonaco, Jr.(*)
Let k(S2)
be a 2-sphere in the 4-sphere
S4
formed by spinning an arc A
about the standard 2-sphere in
S3. And let
( x0, x1, ... , xn : r1,
r2, ... , rm )
be a presentation of
p1(S4 - k(S2))
with x0 the image
of the generator of
p1(S2-A)
under the
inclusion map. Then
( xi ( 0 < i < n+1) :
Sumni=1 (partial rj/partial xi)
= 0, ( 0 < j < m+1) )
is a presentation of
p2(S4 - k(S2))
as a Jp1-module.
(*) Partially supported by the L-O-O-P Fund.
