For spectrally large hyperbolic 3-manifolds with b1=1, the monopole Floer homology is determined by the spectral flow of Dirac operators, which the authors compute from the length spectrum.
auser Classics. Birkh\
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Dirac spectral flow and Floer theory of hyperbolic three-manifolds
For spectrally large hyperbolic 3-manifolds with b1=1, the monopole Floer homology is determined by the spectral flow of Dirac operators, which the authors compute from the length spectrum.