Mathematical Sciences: Problems in Classical Knot Theory

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The principal investigator is currently addressing two areas of research. The first is the application of Casson-Gordon type invariants to problems in link concordance, and, in particular, to questions relating to boundary linking. A second area of research is the study of periodic knots and symmetries of manifolds. Both areas require the development of algebraic tools for describing knots and links and for distinguishing truly distinct knots and links from ones which are merely differently presented. Application of such tools to classify knots and links to within some natural equivalence is a major goal.