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Toplogy and field theories : summer school and conference, May 29-June 8, 2012, Notre Dame University, Notre Dame, Indiana / Stephan Stolz, editor.
- Format:
- Book
- Series:
- Contemporary mathematics (American Mathematical Society). 0271-4132 613
- Contemporary mathematics, 1098-3627 ; 613 0271-4132
- Language:
- English
- Subjects (All):
- Algebraic topology--Congresses.
- Algebraic topology.
- Quantum field theory--Congresses.
- Quantum field theory.
- Physical Description:
- 1 online resource (186 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, 2014.
- Language Note:
- English
- Summary:
- This book is a collection of expository articles based on four lecture series presented during the 2012 Notre Dame Summer School in Topology and Field Theories. The four topics covered in this volume are: Construction of a local conformal field theory associated to a compact Lie group, a level and a Frobenius object in the corresponding fusion category; Field theory interpretation of certain polynomial invariants associated to knots and links; Homotopy theoretic construction of far-reaching generalisations of the topological field theories that Dijkgraf and Witten associated to finite groups; and a discussion of the action of the orthogonal group O(n) on the full subcategory of an n-category consisting of the fully dualisable objects. The expository style of the articles enables non-experts to understand the basic ideas of this wide range of important topics.
- Contents:
- Preface
- Three-Tier CFTs from Frobenius Algebras
- 1. Introduction
- 2. Extended conformal field theory
- 3. Conformal nets and Frobenius algebra objects
- 4. Constructing extended conformal field theories
- Acknowledgements
- References
- Lectures on Knot Homology and Quantum Curves
- Foreword
- 1. Why knot homology?
- 2. The classical -polynomial
- 3. Quantization
- 4. Categorification
- 5. Epilogue: super- -polynomial
- Ambidexterity
- 2. Dijkgraaf-Witten theory
- 3. Local systems and twisted Dijkgraaf-Witten theory
- 4. Ambidexterity
- 5. Ambidexterity in the ( )-local category
- 6. Loop spaces, -divisible groups and character theory
- Dualizability in Low-Dimensional Higher Category Theory
- Introduction
- Higher categories
- 1. Strict n-Categories
- 2. Bicategories
- 3. Higher Categories: Hypotheses of Baez and Dolan
- 3.1. The Homotopy Hypothesis
- 3.2. The stabilization hypothesis
- 3.3. Conclusions about Higher Categories
- 4. Segal Categories
- 4.1. Simplicial objects
- 4.2. The categorical nerve
- 4.3. Segal categories
- 5. Higher Categories: Segal n-categories
- 5.1. Relative Categories
- 5.2. The Segal Category Construction.
- 5.3. Segal -categories
- 6. Dualizability in 2-categories
- 7. Duality in Higher Categories
- 7.1. Symmetric monoidal -categories
- 7.2. Full-Dualizability
- 8. The Cobordism Hypothesis
- 9. Exercises
- Understanding the (1)-action
- 10. Defining categories via generators and relations
- 11. Presentations for low-dimensional bordism categories
- 12. The (1)-action via Presentations
- 13. Unoriented Bordism as a Homotopy Orbit
- 14. Exercises
- Understanding the (2)-action
- 15. The Serre automorphism
- 16. 2-full dualizability and the action of (2)
- 17. Reducing to the study of simply connected 3-types
- 17.1. Whitehead's certain exact sequence and the Î?-functor
- 18. Applying Whitehead's construction to higher categories
- 18.1. Conclusion
- 19. Exercises
- Understanding the (3)-action
- 20. 3-full dualizability and the action of (3)
- 21. The data of an (3) action
- 27.1. First Properties.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 1-4704-1552-6
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