## Differential Geometry, Global Analysis, and Topology: Proceedings of a Special Session of the Canadian Mathematical Society Summer Meeting Held June 1-3, 1990This book contains the proceedings of a special session on differential geometry, global analysis, and topology, held during the Summer Meeting of the Canadian Mathematical Society in June 1990 at Dalhousie University in Halifax. The session featured many fascinating talks on topics of current interest. The articles collected here reflect the diverse interests of the participants but are united by the common theme of the interplay among geometry, global analysis, and topology. Some of the topics include applications to low dimensional manifolds, control theory, integrable systems, Lie algebras of operators, and algebraic geometry. Readers will appreciate the insight the book provides into some recent trends in these areas. |

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### Contents

Complete Metrics of Negative Ricci Curvature on Open 3Manifolds | 1 |

Local Existence of Connections with Prescribed Curvature | 13 |

The Alexander Polynomial via Topological Quantum Field Theory | 27 |

An Equivalence Problem for a TwoForm and a Vector Field on R3 | 41 |

Lie Algebras of First Order Differential Operators in Two Complex Variables | 51 |

Algebraic Geometry and Completely Integrable Hamiltonian Systems | 85 |

On Feedback Equivalence | 105 |

Rational Homotopy Theory and Deformation Problems from Algebraic Geometry | 119 |

Introduction to the Theory of Compact Complex Surfaces | 129 |

Products of Matrices | 157 |

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apply associated assume basis blocks boundary components called classification cocycle cohomology compact complete condition conjugacy classes consider consists constant construction coordinates corresponding curvature curve defined definition deformation denote depend described determined diagram differential operators dimension dimensional divisor eigenvalues elements equal equation equivalence example exists fact finite follows functions geometry germ given gives graded graph hence implies independent integrable intersection invariants irreducible isomorphism lemma Lie algebra line bundle linear manifold Math Mathematical matrix method metric module monomials multiple negative normal Note obtained oriented pair particular partitions points polynomial positive possible problem projection proof proposition rational represented residue restriction satisfy shows simply connected smooth solution space spanned step structure Suppose surface theorem theory translation trivial vector fields zero