Extending Intersection Homology Type Invariants to Non-Witt Spaces.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.