Quadratic functions in geometry, topology, and M-theory

The topological theory 395 5.1. Proof of Theorem 2.17 395 5.2. The topological theory of quadratic functions 404 5.3. The topological 409 5.4. The quadratic functions 414 Appendix A. Simplicial methods 423 A.1. Simplicial set and simplicial objects 423 A.2. Simplicial homotopy groups 425 A.3. Simplicial abelian groups 425 Appendix B. Picard categories and Anderson duality 426 B.1. Anderson duality 426 B.2. Picard categories 428 B.3. Anderson duality and functors of Picard categories 431 Appendix C. Manifolds with corners 432 C.1. t-manifolds 432 C.2. Neat maps and manifolds with corners 433 C.3. Normal bundles and tubular neighborhoods 434 C.4