Department of Mathematics

Geometry and Topology

  •  Nathan Sunukjian, Calvin College
  •  0-concordance of 2-knots
  •  10/13/2016
  •  2:00 PM - 2:50 PM
  •  C304 Wells Hall

A 2-knot is defined to be an embedding of S^2 in S^4. Unlike for knots in S^3, the theory of concordance of 2-knots is trivial. This talk will be framed around the related concept of 0-concordance of 2-knots. It has been conjectured that this is also a trivial theory, that every 2-knot is 0-concordant to every other 2-knot. We will show that this conjecture is false, and in fact there are infinitely many 0-concordance classes. We'll in particular point out how the concept of 0-concordance is related to understanding smooth structures on S^4. The proof will involve invariants coming from Heegaard-Floer homology, and we will furthermore see how these invariants can be used shed light on other properties of 2-knots such as amphichirality and invertibility.

 

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Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
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