Topology of closed one-forms

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The spectral sequence of an equivariant chain complex and homology with local coefficients (2007, background): “The Farber-Novikov spectral sequence has an (E1, d1)-page dual to our (E (1)(X, kZν), d 1 ν)-page, and higher differentials given by certain Massey products; see [12].”
Spectral numbers in Floer theories (2007, unknown): “At least when R is a field, the resulting Novikov chain complex C∗(c) is chain homotopy equivalent to to C∗(M̃) ⊗R[Γ] ΛΓ,ω (see [2]).”
Bieri–Neumann–Strebel–Renz invariants and homology jumping loci (2008, background): “The definition of the Bieri–Neumann–Strebel–Renz (BNSR) invariants was further extended to connected, finite CW-complexes by Farber, Geoghegan, and Schütz [28].”
Floer–Novikov cohomology and the flux conjecture (2006, methodology): “He justified everything necessary in the case of Hamiltonian diffeomorphisms on monotone symplectic manifolds [ F ].”
Persistent homology and Floer-Novikov theory (2015, background): “The difficulty with applying the theory of barcodes to general Floer complexes lies in the fact that, typically, Floer theory is more properly viewed as an infinite dimensional version of Novikov’s Morse theory for closed one-forms ([N81], [Fa04]) rather than of classical Morse theory.”