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Stability of hyperfinite knots
Description:  A hyperfinite knot is an attempt to make sense of limits of sequences of knots with increasing crossing number.
Given a knot invariant taking values on a complete metric space, we define the following quotient space of equivalence classes of knots: two knots are related if, by definition, they have the same value of the invariant. This quotient space of knots inherits the topology of the metric space and, by taking its closure, we can calculate limits of sequences of knots, albeit in the quotient space. If the limit of the sequence of equivalence classes of a particular sequence of knots exists, we call it a hyperfinite knot. Examples of hyperfinite knots have been calculated leaning on the so-called CJKLS invariants of knots.
We wonder if the notion of hyperfinite knot is stable with respect to the different invariants we may choose i.e., if a sequence of knots converges with respect to a given invariant, will it also converge with respect to any other invariant?
In this talk, after presenting some examples of hyperfinite knots stemming from the CJKLS invariants, we report on our current work on stability of hyperfinite knots with respect to these topologies.
Date:  2013-07-02
Start Time:   14:30
Speaker:  Pedro Lopes (IST, Lisboa)
Institution:  Instituto Superior Tecnico - Lisboa
Place:  Sala 5.5
Research Groups: -Geometry
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