Abstract
Many moduli spaces that occur in geometric analysis admit “Fredholm-stratified thin compactifications”, and hence admit a relative fundamental class (RFC), as defined previously by the authors. We extend these results, emphasizing the naturality of the RFC, eliminating the need for a stratification, and proving three compatibility results: the invariants defined by the RFC agree with those defined by pseudo-cycles, the RFC is compatible with cutdown moduli spaces, and the RFC agrees with the virtual fundamental class (VFC) constructed by Pardon via implicit atlases in all cases where both are defined.
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