MULTIVALUED FUNCTIONS AND FUNCTIONALS. AN ANALOGUE OF THE MORSE THEORY

By S. Novikov, I. LetM. 2007

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LECTURES ON FLOER THEORY AND SPECTRAL INVARIANTS OF HAMILTONIAN FLOWS (2006, background): “The Floer homology theory [Fl2], [HS] is the semi-infinite version of the Novikov’s circle valued Morse theory [ N1 ], [N2] of AH on the space L0(M) of contractible free loops.”
Knot homology groups from instantons (2008, unknown): “…reducible connection §2.3 Monotonicity Monotonicity conditionとはtrajectry(Floer homologyの境界写像) の空間の有限性を保証する。 Energy E = ∫ X−Σ |FA|2dvol Kronheimer-Mrowkaの仕事により。 E(X,Σ, P, φ) = 32π2 h∨k+ ∑ β∈R+ β(Φ)c1(o − β )[Σ]− 1 2 ∑ β∈R+ (Σ ·Σ) = 8π2(4h∨k+2⟨Φ, ξ⟩ − ⟨Φ,Φ⟩(Σ ·Σ)) = 8π2(4h∨k+2⟨Φ, l⟩ − ⟨Φ,Φ⟩(Σ ·Σ))”
Persistent homology and Floer-Novikov theory (2015, background): “ 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. Here one considers a closed 1-form αon some ma”