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We will show that the Atiyah-Bott-Goldman volumes of the quotient spaces of
the $\mathsf{PSL}(n,\mathbb{R})$-Hitchin components by the mapping class group
are infinite if $n>2$. We use the bulge deformation of the Hitchin
representations and show that infinitely many images under some sequence of
deformations are disjoint under the projection to the moduli space of Hitchin
representations.
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