7 papers · 1 filter
The rectifiable rectangular peg problem
Tomohiro Asano, Yuichi Ike
We give an affirmative answer to the rectangular peg problem for a large class of continuous Jordan curves that contains all rectifiable curves and Stromquist's locally monotone cu…
-rigidity of Legendrians and coisotropics via sheaf quantization
Tomohiro Asano, Yuichi Ike, Christopher Kuo +1
We prove that in the standard cosphere bundle, for any contact homeomorphism in the closure of the compactly supported contactomorphism group, when the image of a coisotropic subma…
Tamarkin's separation theorem for non-compact objects in cotangent bundles
Yuichi Ike, Tatsuki Kuwagaki
In this short note, we prove a Tamarkin-type separation theorem for possibly non-compact subsets in cotangent bundles.
Regular Lagrangians are smooth Lagrangians
Tomohiro Asano, Stéphane Guillermou, Yuichi Ike +1
We prove that for any element in the -completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its -support is a smooth Lagrangian…
Lagrangian cobordism and shadow distance in Tamarkin category
Tomohiro Asano, Yuichi Ike, Wenyuan Li
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…
Microlocal categories over Novikov rings
Yuichi Ike, Tatsuki Kuwagaki
In this paper, we define a family of categories for each Weinstein manifold, which is an enhanced version of the category first introduced by Tamarkin. Using our categories, for an…