On equivalence of two constructions of invariants of Lagrangian submanifolds

Abstract

We give the construction of symplectic invariants which incorporates both the "infinite dimensional" invariants constructed by Oh in 1997 and the "finite dimensional" ones constructed by Viterbo in 1992.

Geodesics on the space of Lagrangian submanifolds in cotangent bundles

“…Theorem 2 complements the conclusion made at the end of Section 7 of [7] that, if c(µ, L), c(1, L) are Viterbo's invariants of L (see [10] …”

Coisotropic rigidity and C0-symplectic geometry

“…In [25], Viterbo defined Lagrangian spectral invariants on R 2n and cotangent bundles via generating functions. Then Oh [19] defined similar invariants via Lagrangian Floer homology in cotangent bundles which have been proven to coincide with Viterbo's invariants by Milinković [16]. They have been adapted to the compact case by Leclercq [12] for weakly exact Lagrangians and Leclercq-Zapolsky [13] for monotone Lagrangians.…”

Comparison of spectral invariants in Lagrangian and Hamiltonian Floer theory

“…The upper diagram is (10) and the lower is Albers' (8). For given α ∈ H * (P) and β ∈ H * (L), let us define the sets:…”

“…This construction is based on Viterbo's idea for generating functions defined in the case of cotangent bundle (see [21]). It turned out that Oh's and Viterbo's invariants are in fact the same, see [9,10]. Oh proved in [15] that these invariants are independent both of the choice of almost complex structure J (which enters the definition of Floer homology) and, after a certain normalization, on the choice of H as long as φ 1 H (L 0 ) = L 1 .…”