Preliminaries: Note on conventions Basic homotopy notions Surgery below the middle dimension Appendix: Applications Simple Poincare complexes The main theorem: Statement of results An important special case The even-dimensional case The odd-dimensional case The bounded odd-dimensional case The bounded even-dimensional case Completion of the proof Patterns of application: Manifold structures on Poincare complexes Applications to submanifolds Submanifolds: Other techniques Separating submanifolds Two-sided submanifolds One-sided submanifolds Calculations and applications: Calculations: Surgery obstruction groups Calculations: The surgery obstructions Applications: Free actions on spheres General remarks An extension of the Atiyah-Singer $G$-signature theorem Free actions of $S^1$ Fake projective spaces (real) Fake lens spaces Applications: Free uniform actions on euclidean space Fake tori Polycyclic groups Applications to 4-manifolds Postscript: Further ideas and suggestions: Recent work Function space methods Topological manifolds Poincare embeddings Homotopy and simple homotopy Further calculations Sullivan's results Reformulations of the algebra Rational surgery References Index.

Surgery on compact manifolds

Introduction to BIBDs.- Symmetric BIBDs.- Difference sets and automorphisms.- Hadamard matrices and designs.- Resolvable BIBDs.- Steiner triple systems.- Mutually orthogonal Latin squares.- Pairwise balanced designs.- t-designs.- Orthogonal arrays and codes.- Index.

/pdf/combinatorial-designs-constructions-and-analysis-3mofrky3c7.pdf

Combinatorial Designs: Constructions and Analysis

Algebraic coding theory has in recent years been increasingly applied to the study of combinatorial designs. This book gives an account of many of those applications together with a thorough general introduction to both design theory and coding theory - developing the relationship between the two areas. The first half of the book contains background material in design theory, including symmetric designs and designs from affine and projective geometry, and in coding theory, coverage of most of the important classes of linear codes. In particular, the authors provide a new treatment of the Reed-Muller and generalized Reed-Muller codes. The last three chapters treat the applications of coding theory to some important classes of designs, namely finite planes, Hadamard designs and Steiner systems, in particular the Witt systems. The book is aimed at mathematicians working in either coding theory or combinatorics - or related areas of algebra. The book is, however, designed to be used by non-specialists and can be used by those graduate students or computer scientists who may be working in these areas.

Designs and their codes

(1991). The Search for a Finite Projective Plane of Order 10. The American Mathematical Monthly: Vol. 98, No. 4, pp. 305-318.

/pdf/the-search-for-a-finite-projective-plane-of-order-10-ehqwv7o69d.pdf

The search for a finite projective plane of order 10

Designs and their codes: Bibliography

Normal Completions of Incidence Matrices

Let it be required to arrange v elements into v sets such that each set contains exactly k distinct elements and such that each pair of sets has exactly λ elements in common (0 < λ < k < v). This problem we refer to as the v, k,λ combinatorial problem.

Cyclic incidence matrices

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Normal Completions of Incidence Matrices

Cyclic incidence matrices