Lowell Jones

On the Isomorphism Conjecture in algebraic K -theory

The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RΓ, where Γ is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed Riemannian manifolds with strictly negative sectional curvature and arbitrary coefficient rings R. If R is regular this leads to a concrete calculation of low dimensional K-theory groups of RΓ in terms of the K-theory of R and the homology of the group.

The Converse to the Fixed Point Theorem of P. A. Smith: I

Microwave energy is used for sealing polymeric film material particularly the sealing of film material in the form of flexible containers.

Patch Spaces: A Geometric Representation for Poincare Spaces

Section Page Preface 306 ?1. Preliminaries 307 2. Elementary properties 310 ? 3. Surgery on patch spaces 311 ?4. Changing patch structures 323 ?5. Obstruction to transversality 329 ? 6. The existence and uniqueness of patch space structures on Poincare duality spaces 334 S 7. Applications 338 (7.0) Surgery composition formula (7.1) Surgery product theorem (7.2) Computing cobordism classes of Poincare spaces (7.3) Representing homology classes by Poincare spaces (7.4) Characteristic variety theorem and homotopy type of BSF (7.11) Patch space structures for spaces which are Poincare mod a set of primes

A FOLIATED SQUEEZING THEOREM FOR GEOMETRIC MODULES

We prove a foliated control theorem for automorphisms of geometric modules. This is the analogue of a result for h-cobordism

Immersions of surfaces into surfaces

Abstract IMMERSIONS of a compact surface into another surface are classified up to a “weak” topological conjugacy equivalence. The main theorem of this paper says that two immersions from a compact surface into an open surface are “weakly” conjugate if and only if they are regularly homotopic.