The Kauffman bracket skein module of the connected sum of two genus-one handlebodies is determined over Z[q^{±1}].
Kaplansky, Infinite abelian groups , Univ
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Kauffman bracket skein module of the connected sum of two solid tori
The Kauffman bracket skein module of the connected sum of two genus-one handlebodies is determined over Z[q^{±1}].