Work

Lagrangian cobordism and shadow distance in Tamarkin category

Year: 2025

Type: article

Abstract: We study exact Lagrangian cobordisms between exact Lagrangians in a cotangent bundle in the sense of Arnol’d, using microlocal theory of sheaves. We construct a sheaf quantization for an exact Lagrangian cobordism between Lagrangians with conical ends, prove an iterated cone decomposition of the sheaf quantization for cobordisms with multiple ends, and show that the interleaving distance of sheaves is bounded by the shadow distance of the cobordism. Using the result, we prove a rigidity result on Lagrangian intersection by estimating the energy cost of splitting and connecting Lagrangians through cobordisms.

Source: Selecta Mathematica

DOI: 10.1007/s00029-025-01034-9

Authors: Tomohiro Asano, Yuichi Ike, Wenyuan Li

Institutions: Kyoto University, Research Institute for Mathematical Sciences, Kyoto University, Kyushu University, University of Southern California

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: University of Southern California, Japan Society for the Promotion of Science, Core Research for Evolutional Science and Technology