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Triangulating a Cappell-Shaneson knot complement

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 Added by Ryan Budney
 Publication date 2011
  fields
and research's language is English




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We show that one of the Cappell-Shaneson knot complements admits an extraordinarily small triangulation, containing only two 4-dimensional simplices.



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Given a grid diagram for a knot or link K in $S^3$, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry, but rather builds on the combinatorial definition of grid homology. We inductively define models for the moduli spaces of pseudo-holomorphic strips and disk bubbles, and patch them together into a framed flow category. The inductive step relies on the vanishing of an obstruction class that takes values in a complex of positive domains with partitions.
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