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Tables of Contents for Factorizable Sheaves and Quantum Groups
Chapter/Section Title
Page #
Page Count
Introduction
1
4
Acknowledgement
5
1
Part 0. OVERVIEW
6
44
1. Introduction
6
5
Chapter 1. Local
11
16
2. The category C
11
4
3. Braiding local systems
15
4
4. Factorizable sheaves
19
1
5. Tensor product
20
3
6. Vanishing cycles
23
4
Chapter 2. Global (genus 0)
27
13
7. Cohesive local systems
27
3
8. Gluing
30
1
9. Semiinfinite cohomology
31
2
10. Conformal blocks (genus 0)
33
2
11. Integration
35
1
12. Regular representation
36
1
13. Regular sheaf
37
3
Chapter 3. Modular
40
10
14. Heisenberg local system
40
6
15. Fusion structures on FS
46
2
16. Conformal blocks (higher genus)
48
2
Part I. INTERSECTION COHOMOLOGY OF REAL ARRANGEMENTS
50
21
1. Introduction
50
1
2. Topological preliminaries
51
4
3. Vanishing cycles functors
55
8
4. Computations for standard sheaves
63
8
Part II. CONFIGURATION SPACES AND QUANTUM GROUPS
71
51
1. Introduction
71
2
Chapter 1. Algebraic discussion
73
16
2. Free algebras and bilinear forms
73
9
3. Hochschild complexes
82
2
4. Symmetrization
84
3
5. Quotient algebras
87
2
Chapter 2. Geometric discussion
89
21
6. Diagonal stratification and related algebras
89
5
7. Principal stratification
94
6
8. Standard sheaves
100
10
Chapter 3. Fusion
110
6
9. Additivity theorem
110
2
10. Fusion and tensor products
112
4
Chapter 4. Category C
116
6
11. Simply laced case
116
3
12. Non-simply laced case
119
3
Part III. TENSOR CATEGORIES ARISING FROM CONFIGURATION SPACES
122
51
1. Introduction
122
2
Chapter 1. Category FS
124
10
2. Space A
124
2
3. Braiding local system I
126
2
4. Factorizable sheaves
128
2
5. Finite sheaves
130
2
6. Standard sheaves
132
2
Chapter 2. Tensor structure
134
16
7. Marked disk operad
134
4
8. Cohesive local systems (K)I
138
1
9. Factorizable sheaves over (K)A
139
3
10. Gluing
142
3
11. Fusion
145
5
Chapter 3. Functor Phi
150
12
12. Functor Phi
150
9
13. Main properties of Phi
159
3
Chapter 4. Equivalence
162
11
14. Truncation functors
162
3
15. Rigidity
165
2
16. Steinberg sheaf
167
2
17. Equivalence
169
1
18. The case of generic
170
3
Part IV. LOCALIZATION OVER P(1)
173
24
1. Introduction
173
1
Chapter 1. Gluing over P(1)
174
6
2. Cohesive local system
174
2
3. Gluing
176
4
Chapter 2. Semiinifinite cohomology
180
8
4. Semiinifinite functors Ext and Tor in C
180
4
5. Some calculations
184
4
Chapter 3. Global sections
188
9
6. Braiding and balance in C and FS
188
1
7. Global sections over A(K)
189
1
8. Global sections over P
190
3
9. Application to conformal blocks
193
4
Part V. MODULAR STRUCTURE ON THE CATEGORY FS
197
55
1. Introduction
197
2
Chapter 1. Heisenberg local system
199
20
2. Notations and statement of the main result
199
3
3. The scheme of construction
202
2
4. The universal line bundle
204
3
5. The universal local system
207
9
6. Factorization isomorphisms
216
3
Chapter 2. The modular property of the Heisenberg system
219
12
7. Degeneration of curves: recollections and notations
219
2
8. Proof of Theorem 7.6(a)
221
3
9. Proof of Theorem 7.6(b)
224
7
Chapter 3. Regular representation
231
4
10. A characterization of the regular bimodule
231
2
11. The adjoint representation
233
2
Chapter 4. Quadratic degeneration in genus zero
235
7
12. I-sheaves
235
1
13. Degenerations of quadrics
236
1
14. The I-sheaf R
237
2
15. Convolution
239
3
Chapter 5. Modular functor
242
7
16. Gluing over C
242
4
17. Degeneration of factorizable sheaves
246
2
18. Global sections over C
248
1
Chapter 6. Integral representations of conformal blocks
249
3
19. Conformal blocks in arbitrary genus
249
3
References
252
2
Index of Notation
254
29
Index of Terminology
283