2025/11/12 by Asplund, Johan, Deshmukh, Yash, Pieloch, Alex
#57R58 53D12 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2511.09548
An exact Lagrangian submanifold L ⊂ X2n in a Weinstein sector is called a nearby Lagrangian cocore if it avoids all Lagrangian cocores and is equal to a shifted Lagrangian cocore at infinity. Let k be the dimension of the core of the subcritical part of X. For n ≥ 2k+2 we prove that that the inclusion of L followed by the retract to the Lagrangian core of X and the quotient by the (n-k-1)-skeleton of the core, is null-homotopic. As a consequence, in many examples, a nearby Lagrangian cocore is smoothly isotopic (rel boundary) to a Lagrangian cocore in the complement of the missed Lagrangian cocores. The proof uses the spectral wrapped Donaldson-Fukaya category with coefficients in the ring spectrum representing the bordism group of higher connective covers of the orthogonal group.