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

Statements of the main results Reformulation of the main results Reduction steps in proving the main theorems Test functions Haar measure Tail estimates Large $N$ limits and Fredholm determinants Several variables Equidistribution Monodromy of families of curves Monodromy of some other families GUE discrepancies in various families Distribution of low-lying Frobenius eigenvalues in various families Appendix AD: Densities Appendix AG: Graphs References.

Random matrices, Frobenius eigenvalues, and monodromy

A new construction of symplectic manifolds

then M is said to be a differentiable manifold with almost complex structure. (Tensor fields of the form given above may exist only for some manifolds with even dimension.) We shall call φ the fundamental collineation of the almost complex structure. The set of differentiable manifolds with almost complex structure is wider than the set of complex manifolds. Every differentiable manifold with almost complex structure φ admits a poistive definite Riemannian metric g such that

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On differentiable manifolds with certain structures which are closely related to almost contact structure i

Basic Hodge Theory.- Compact Kahler Manifolds.- Pure Hodge Structures.- Abstract Aspects of Mixed Hodge Structures.- Mixed Hodge Structures on Cohomology Groups.- Smooth Varieties.- Singular Varieties.- Singular Varieties: Complementary Results.- Applications to Algebraic Cycles and to Singularities.- Mixed Hodge Structures on Homotopy Groups.- Hodge Theory and Iterated Integrals.- Hodge Theory and Minimal Models.- Hodge Structures and Local Systems.- Variations of Hodge Structure.- Degenerations of Hodge Structures.- Applications of Asymptotic Hodge Theory.- Perverse Sheaves and D-Modules.- Mixed Hodge Modules.

Hsien-Chung Wang

Papers

On Contact Manifolds

Complex parallisable manifolds

Discrete subgroups of solvable lie groups i

Homogeneous Spaces with Non-Vanishing Euler Characteristics

Commutators in a semi-simple Lie group