This volume includes both survey and research articles on major advances and future developments in geometry and topology. Papers include those presented as part of the 5th Aarhus Conference - a meeting of international participants held in connection with ICM Berlin in 1998 - and related papers on the subject. This collection of papers is aptly published in the ""Contemporary Mathematics"" series, as the works represent the state of research and address areas of future development in the area of manifold theory and geometry. The survey articles in particular would serve well as supplemental resources in related graduate courses.

Table of Contents:
Complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups by A. Baker and C. Ozel Unique continuation property of Dirac operators, revisited by B. Booss-Bavnbek Torus actions determined by simple polytopes by V. M. Buchstaber and T. E. Panov The Torelli group action on representation spaces by S. E. Cappell, R. Lee, and E. Y. Miller Notes on Seiberg-Witten-Floer theory by A. L. Carey and B.-L. Wang Stability for holomorphic spheres and Morse theory by R. L. Cohen, J. D. S. Jones, and G. B. Segal Embedded minimal surfaces without area bounds in 3-manifolds by T. H. Colding and W. P. Minicozzi II The cyclotomic trace for symmetric monoidal categories by B. I. Dundas Isoparametric submanifolds and symmetric spaces by J.-H. Eschenburg Obstructions to homotopy invariance in parametrized fixed point theory by R. Geoghegan, A. Nicas, and D. Schutz Lagrangian path intersections and the Leray index by M. de Gosson Associativity in two-cell complexes by B. Gray Nonnegative curvature and normal holonomy in open manifolds by L. Guijarro Compactifying infinite group actions by I. Hambleton and E. K. Pedersen Positive and negative results concerning the Gromov-Lawson-Rosenberg conjecture by M. Joachim and T. Schick Stable modules and the structure of Poincare 3-complexes by F. E. A. Johnson The equivariant cohomology ring of the moduli space of vector bundles over a Riemann surface by Y.-H. Kiem Poincare embeddings of spheres by J. R. Klein Beginning of analysis on Alexandrov spaces by K. Kuwae, Y. Machigashira, and T. Shioya Negative curvature and symplectic submanifolds by J. Lohkamp On the universal space for group actions with compact isotropy by W. Luck and D. Meintrup The circle transfer and K-theory by I. Madsen and C. Schlichtkrull Finite groups possessing gap modules by M. Morimoto, T. Sumi, and M. Yanagihara Smith equivalence of group modules and the Laitinen conjecture. A survey by K. Pawalowski Controlled algebraic K-theory, a survey by E. K. Pedersen Taut codimension one spheres of odd order by L. R. Taylor Bivariant Riemann Roch theorems by B. Williams.