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**The second homotopy group of a spun knot**

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**Samuel J. Lomonaco, Jr.**^{(*)}

**
Let k(S**^{2})
be a 2-sphere in the 4-sphere
S^{4}
formed by spinning an arc A
about the standard 2-sphere in
S^{3}. And let

**
**

**
( x**_{0}, x_{1}, ... , x_{n} : r_{1},
r_{2}, ... , r_{m} )
**
**

be a presentation of
p_{1}(S^{4} - k(S^{2}))
with x_{0} the image
of the generator of
p_{1}(S^{2}-A)
under the
inclusion map. Then

( x_{i} ( 0 < i < n+1) :
Sum^{n}_{i=1} (partial r_{j}/partial x_{i})
= 0, ( 0 < j < m+1) )

is a presentation of
p_{2}(S^{4} - k(S^{2}))
as a Jp_{1}-module.
(*) Partially supported by the L-O-O-P Fund.