Towards Proving the Novikov Conjecture
David Rosenthal, Department of Mathematics and Computer Science, St. John’s College of Liberal Arts and Sciences
Abstract
Topology is the study of those properties of geometric spaces that are unaffected by shrinking or twisting or other continuous deformations. It is often possible to translate questions about geometric spaces into the language of abstract algebra. Algebraic topology is the branch of topology that makes use of these connections to solve geometric problems. One of the goals in topology is to classify a special class of spaces called manifolds. The algebraic K- and L-theory groups contain important geometric information about manifolds. However, determining these groups is a very complex problem. The well-known Novikov Conjecture offers one approach to understanding these groups for high-dimensional manifolds. In this project, techniques are developed to prove the Novikov Conjecture in several important cases.