TAILIEUCHUNG - Đề tài " Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups "

We prove that the sequence of projective quantum SU(n) representations of the mapping class group of a closed oriented surface, obtained from the projective flat SU(n)-Verlinde bundles over Teichm¨ller space, is asymptotically u faithful. That is, the intersection over all levels of the kernels of these representations is trivial, whenever the genus is at least 3. For the genus 2 case, this intersection is exactly the order 2 subgroup, generated by the hyper-elliptic involution, in the case of even degree and n = 2. Otherwise the intersection is also trivial in the genus 2 case. . | Annals of Mathematics Asymptotic faithfulness of the quantum SU n representations of the mapping class groups By Jorgen Ellegaard Andersen Annals of Mathematics 163 2006 347 368 Asymptotic faithfulness of the quantum SU n representations of the mapping class groups By J0RGEN Ellegaard Andersen Abstract We prove that the sequence of projective quantum SU n representations of the mapping class group of a closed oriented surface obtained from the projective flat SU n -Verlinde bundles over Teichmuller space is asymptotically faithful. That is the intersection over all levels of the kernels of these representations is trivial whenever the genus is at least 3. For the genus 2 case this intersection is exactly the order 2 subgroup generated by the hyper-elliptic involution in the case of even degree and n 2. Otherwise the intersection is also trivial in the genus 2 case. 1. Introduction In this paper we shall study the finite dimensional quantum SU n representations of the mapping class group of a genus g surface. These form the only rigorously constructed part of the gauge-theoretic approach to topological quantum field theories in dimension 3 which Witten proposed in his seminal paper W1 . We discovered the asymptotic faithfulness property for these representations by studying this approach which we will now briefly describe leaving further details to Sections 2 and 3 and the references given there. Let s be a closed oriented surface of genus g 2 and p a point on s. Fix d E Z nZ ZSU n in the center of SU n . Let M be the moduli space of flat SU n -connections on s p with holonomy d around p. By applying geometric quantization to the moduli space M one gets a certain finite rank vector bundle over Teichmuller space T which we will call the Verlinde bundle Vk at level k where k is any positive integer. The fiber of this bundle over a point Ơ eT is Vkyơ H MƠ L g where Mơ is M equipped with a complex structure induced from Ơ and cơ is an ample generator of the Picard group

• Thạc sĩ - Tiến sĩ - Cao học
• Asymptotic faithfulness
• subjects 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