TAILIEUCHUNG - Đề tài " Holomorphic disks and topological invariants for closed three-manifolds "

Holomorphic disks and topological invariants for closed three-manifolds ´ ´ ´ By Peter Ozsvath and Zoltan Szabo* Abstract The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y , equipped with a Spinc structure. Given a Heegaard splitting of Y = U0 ∪Σ U1 , these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of Σ relative to certain totally real subspaces associated to U0 and U1 . 1. Introduction Let Y be a connected, closed, oriented three-manifold, equipped with a Spin structure s. . | Annals of Mathematics Holomorphic disks and topological invariants for closed three-manifolds By Peter Ozsv ath and Zolt an Szab o Annals of Mathematics 159 2004 1027-1158 Holomorphic disks and topological invariants for closed three-manifolds By Peter OzsvATH and Zoltán Szabo Abstract The aim of this article is to introduce certain topological invariants for closed oriented three-manifolds Y equipped with a Spinc structure. Given a Heegaard splitting of Y U0 Uy U1 these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of s relative to certain totally real subspaces associated to U0 and U1. 1. Introduction Let Y be a connected closed oriented three-manifold equipped with a Spinc structure s. Our aim in this paper is to define certain Floer homology groups HF Y s HF Y s HF- Y s HF Y s and HFred Y s using Heegaard splittings of Y . For calculations and applications of these invariants we refer the reader to the sequel 28 . Recall that a Heegaard splitting of Y is a decomposition Y U0 Uy U1 where U0 and U1 are handlebodies joined along their boundary s. The splitting is determined by specifying a connected closed oriented two-manifold s of genus g and two collections a1 . ag and 1 . @g of simple closed curves in s. The invariants are defined by studying the g-fold symmetric product of the Riemann surface s a space which we denote by Symg s . this is the quotient of the g-fold product of s which we denote by sxg by the action of the symmetric group on g letters. There is a quotient map n sxg Symg s . Symg s is a smooth manifold in fact a complex structure on s naturally gives rise to a complex structure on Symg s for which n is a holomorphic map. PSO was supported by NSF grant number DMS-9971950 and a Sloan Research Fellowship. ZSz was supported by NSF grant number DMS-9704359 a Sloan Research Fellowship and a Packard Fellowship. 1028 PETER OZSVATH AND ZOLTÁN SZABO In 7 Floer considers a homology theory defined for a symplectic

• Thạc sĩ - Tiến sĩ - Cao học
• Holomorphic disks
• subjects of mathematics
• Annals of Mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center