Consider a space
, such as a
compact space of
–holomorphic
stable maps, that is the zero set of a Kuranishi atlas. This
note explains how to define the virtual fundamental class of
by representing
via the zero
set of a map
,
where
is a finite-dimensional vector space and the domain
is an oriented, weighted branched topological manifold. Moreover,
is equivariant under the action of the global isotropy group
on
and
. This tuple
together with a
homeomorphism from
to
forms a single finite-dimensional model (or chart) for
. The
construction assumes only that the atlas satisfies a topological version of the index condition
that can be obtained from a standard, rather than a smooth, gluing theorem. However, if
is presented as the zero
set of an
–Fredholm
operator on a strong polyfold bundle, we outline a much more direct construction of the branched
manifold
that
uses an
–smooth
partition of unity.
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