TY  - BOOK
AU  - Pelayo,Alvaro
TI  - Symplectic Actions of 2-Tori on 4-Manifolds
T2  - Memoirs of the American Mathematical Society
SN  - 9781470405731
AV  - QA649 -- .P453 2009eb 
U1  - 516.3/62 
PY  - 2010///
CY  - Providence
PB  - American Mathematical Society
KW  - Symplectic manifolds
KW  - Low-dimensional topology
KW  - Torus (Geometry)
KW  - Electronic books
N1  - Intro -- Contents -- Acknowledgements -- Chapter 1. Introduction -- Chapter 2. The orbit space -- 2.1. Symplectic form on the T-orbits -- 2.2. Stabilizer subgroup classification -- 2.3. Orbifold structure of M/T -- 2.4. A flat connection for the projection M M/T -- 2.5. Symplectic tube theorem -- Chapter 3. Global model -- 3.1. Orbifold coverings of M/T -- 3.2. Symplectic structure on M/T -- 3.3. Model of (M,  ): Definition -- 3.4. Model of (M,): Proof -- Chapter 4. Global model up to equivariant diffeomorphisms -- 4.1. Generalization of Kahn's theorem -- 4.2. Smooth equivariant splittings -- 4.3. Alternative model -- Chapter 5. Classification: Free case -- 5.1. Monodromy invariant -- 5.2. Uniqueness -- 5.3. Existence -- 5.4. Classification theorem -- Chapter 6. Orbifold homology and geometric mappings -- 6.1. Geometric torsion in homology of orbifolds -- 6.2. Geometric isomorphisms -- 6.3. Symplectic and torsion geometric maps -- 6.4. Geometric isomorphisms: Characterization -- Chapter 7. Classification -- 7.1. Monodromy invariant -- 7.2. Uniqueness -- 7.3. Existence -- 7.4. Classification theorem -- Chapter 8. The four-dimensional classification -- 8.1. Two families of examples -- 8.2. Classification statement -- 8.3. Proof of Theorem 8.2.1 -- 8.4. Corollaries of Theorem 8.2.1 -- Chapter 9. Appendix: (sometimes symplectic) orbifolds -- 9.1. Bundles, connections -- 9.2. Coverings -- 9.3. Differential and symplectic forms -- 9.4. Orbifold homology, Hurewicz map -- 9.5. Classification of orbisurfaces -- Bibliography
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114172
ER  -