單調拉格朗日流形與辛拓樸;Monotone Lagrangian Submanifolds and Symplectic Topology

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/63168

Title:	單調拉格朗日流形與辛拓樸;Monotone Lagrangian Submanifolds and Symplectic Topology
Authors:	姚美琳
Contributors:	國立中央大學數學系
Keywords:	數學
Date:	2012-12-01
Issue Date:	2014-03-17 14:20:44 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	研究期間：10108~10207;In this research project, we focus on monotone Lagrangian tori of general dimensions, and study them from the perspective of surgery. In the first year we will develop surgical constructions of twist tori in R2n. For the second year we will explore new Hamiltonian isotopy invariants associated to the surgery. We will also examine the relation between the surgery and other invariants of Lagrangian submanifolds. Starting from the third year we will extend our study to the global case and exploring the interplay between the topology of symplectic manifolds and that of their monotone Lagrangian submanifolds. In the third year we will consider Stein manifolds and their monotone Lagrangian submanifolds. In the fourth year we will extend our investigation to the compact Kahler case. We will focus on some model examples including the projective spaces and product manifolds of spheres.
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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