Memoirs of the American Mathematical Society; Vol.207, N 971 (Providence, 2010). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаHamilton M.D. Locally toric manifolds and singular Bohr-Sommerfeld leaves. - Providence: American Mathematical Society, 2010. - v, 60 p. - (Memoirs of the American Mathematical Society; Vol.207, N 971). - Bibliogr.: p.59-60. - ISBN 978-0-8218-4714-5; ISSN 0065-9266
 

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Оглавление / Contents
 
Chapter 1  Introduction ......................................... 1

1.1  Methods .................................................... 2

Chapter 2  Background ........................................... 5

2.1  Connections ................................................ 5
2.2  Sheaves and cohomology ..................................... 7
2.3  Toric manifolds ............................................ 9
2.4  Geometric quantization and polarizations .................. 10
2.5  Examples .................................................. 13
2.6  Aside: Rigidity of Bohr-Sommerfeld leaves ................. 14

Chapter 3  The cylinder ........................................ 15

3.1  Flat sections and Bohr-Sommerfeld leaves .................. 15
3.2  Sheaf cohomology .......................................... 16
3.3  Brick wall covers ......................................... 19
3.4  Mayer-Vietoris ............................................ 24
3.5  Refinements and covers: Scaling the brick wall ............ 26

Chapter 4  The complex plane ................................... 29

4.1  The sheaf of sections flat along the leaves ............... 29
4.2  Cohomology ................................................ 30
4.3  Mayer-Vietoris ............................................ 34

Chapter 5  Example: S2 ......................................... 35

Chapter 6  The multidimensional case ........................... 37

6.1  The model space ........................................... 37
6.2  The flat sections ......................................... 37
6.3  Multidimensional Mayer-Vietoris ........................... 38

Chapter 7  A better way to calculate cohomology ................ 41

7.1  Theory .................................................... 41
7.2  The case of one dimension ................................. 45
7.3  The structure of the coming calculation ................... 45
7.4  The case of several dimensions: Non-singular .............. 46
7.5  The partially singular case ............................... 49

Chapter 8  Piecing and glueing ................................. 51

8.1  Necessary sheaf theory .................................... 51
8.2  The induced map on cohomology ............................. 52
8.3  Patching together ......................................... 54

Chapter 9  Real and Kahler polarizations compared .............. 57

Bibliography ................................................... 59


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