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Knot concordance and symmetriesGeometry/Topology
|Speaker:||Swatee Naik, UN Reno|
|Start time:||Tue, Mar 6 2012, 3:10PM|
A knot is an embedding of a circle in the three dimensional sphere. Knot concordance is an equivalence relation under which knots bounding a smooth disk in the 4-ball are considered trivial. Concordance classes form a countable, abelian group which has elements of order two represented by negative amphicheiral knots, and it has infinite order elements. A nontrivial quotient of this group is a direct sum of countably many cyclic groups of orders two, four and infinity. Other than this, not much is known about its group structure. We will discuss order in the concordance group as well as an interplay between knot concordance and symmetries such as cyclic periodicity and amphicheirality.