Extending Intersection Homology Type Invariants to Non-Witt Spaces.
Banagl, Markus.
Extending Intersection Homology Type Invariants to Non-Witt Spaces. - 1st ed. - 1 online resource (101 pages) - Memoirs of the American Mathematical Society ; v.160 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Chapter 1. Introduction -- 1. History -- 2. Motivation -- 3. The Main Result: A Postnikov System of Lagrangian Structures -- 4. Consequences: Characteristic Classes -- 5. Ordered Resolutions - A Model Construction -- 6. Applications -- 7. Further Developments -- 8. Sign Questions -- 9. Some Remarks on Coefficients -- 10. Acknowledgments -- 11. Notation -- Chapter 2. The Algebraic Framework -- 1. The Lifting Obstruction -- 2. The Category of Self-Dual Sheaves Compatible with IH -- 3. Lagrangian Structures -- 4. Extracting Lagrangian Structures from Self-Dual Sheaves -- 5. Lagrangian Structures as Building Blocks for Self-Dual Sheaves -- 6. A Postnikov system -- Chapter 3. Ordered Resolutions -- 1. The Purpose of the Construction -- 2. Definitions -- 3. The PL Construction -- 4. Inductive Singularization of a Manifold -- Chapter 4. The Cobordism Group Ω[sup(SD)][sub(*)] -- 1. The Closed Objects -- 2. The Admissible Cobordisms -- 3. The Cobordism Invariance of σ -- 4. Relation to Witt Space Cobordism -- Chapter 5. Lagrangian Structures and Ordered Resolutions -- 1. Statement of Result -- 2. The inductive set-up -- 3. Construction of a nonsingular pairing on H[sup(k)](j*S[sup[.)] -- 4. Stalks of H[sup(k)](j*S[sup[.)] as the hypercohomology of the link of Σ -- 5. The restriction of L[[sup(.)](X[sup((m))]) to V(x) is self-dual -- 6. The construction of a Lagrangian subsheaf of H[sup(k)](j*S[sup[.)] -- 7. The definition of L[sup(.)](X[sup((m+1))]) -- Appendix A. On Signs -- Bibliography.
9781470403584
Intersection homology theory.
Duality theory (Mathematics).
Electronic books.
QA612.32 -- .B36 2002eb
510 s;514/.23
Extending Intersection Homology Type Invariants to Non-Witt Spaces. - 1st ed. - 1 online resource (101 pages) - Memoirs of the American Mathematical Society ; v.160 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Chapter 1. Introduction -- 1. History -- 2. Motivation -- 3. The Main Result: A Postnikov System of Lagrangian Structures -- 4. Consequences: Characteristic Classes -- 5. Ordered Resolutions - A Model Construction -- 6. Applications -- 7. Further Developments -- 8. Sign Questions -- 9. Some Remarks on Coefficients -- 10. Acknowledgments -- 11. Notation -- Chapter 2. The Algebraic Framework -- 1. The Lifting Obstruction -- 2. The Category of Self-Dual Sheaves Compatible with IH -- 3. Lagrangian Structures -- 4. Extracting Lagrangian Structures from Self-Dual Sheaves -- 5. Lagrangian Structures as Building Blocks for Self-Dual Sheaves -- 6. A Postnikov system -- Chapter 3. Ordered Resolutions -- 1. The Purpose of the Construction -- 2. Definitions -- 3. The PL Construction -- 4. Inductive Singularization of a Manifold -- Chapter 4. The Cobordism Group Ω[sup(SD)][sub(*)] -- 1. The Closed Objects -- 2. The Admissible Cobordisms -- 3. The Cobordism Invariance of σ -- 4. Relation to Witt Space Cobordism -- Chapter 5. Lagrangian Structures and Ordered Resolutions -- 1. Statement of Result -- 2. The inductive set-up -- 3. Construction of a nonsingular pairing on H[sup(k)](j*S[sup[.)] -- 4. Stalks of H[sup(k)](j*S[sup[.)] as the hypercohomology of the link of Σ -- 5. The restriction of L[[sup(.)](X[sup((m))]) to V(x) is self-dual -- 6. The construction of a Lagrangian subsheaf of H[sup(k)](j*S[sup[.)] -- 7. The definition of L[sup(.)](X[sup((m+1))]) -- Appendix A. On Signs -- Bibliography.
9781470403584
Intersection homology theory.
Duality theory (Mathematics).
Electronic books.
QA612.32 -- .B36 2002eb
510 s;514/.23