  An affine monoid is an additive monoid which is cancellative, pointed and
finitely generated. An affine monoid $\Lambda$ has the partial order defined by
$\lambda \le \lambda + \mu$. The Frobenius complex is the order complex of an
open interval of $\Lambda$ with respect to this partial order. The reduced
homology of the Frobenius complex is related to the torsion group of the monoid
algebra $K[\Lambda]$. In this paper, we pay attention to homotopy types of
Frobenius complexes, and we express the homotopy types of the Frobenius
complexes of $\Lambda$ in terms of those of $\Lambda_1$ and $\Lambda_2$ when
$\Lambda$ is an affine monoid obtained by gluing two affine monoids $\Lambda_1$
and $\Lambda_2$ with one relation. We also state an application to the
Poincar\'e series of the torsion group of the monoid algebra.
