Volume 19, issue 4 (2019)

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Truncated Heegaard Floer homology and knot concordance invariants

Linh Truong

Algebraic & Geometric Topology 19 (2019) 1881–1901
Abstract

We construct a sequence of smooth concordance invariants ${\nu }_{n}\left(K\right)$ defined using truncated Heegaard Floer homology. The invariants generalize the concordance invariants $\nu$ of Ozsváth and Szabó and ${\nu }^{+}$ of Hom and Wu. We exhibit an example in which the gap between two consecutive elements in the sequence ${\nu }_{n}$ can be arbitrarily large. We also prove that the sequence ${\nu }_{n}$ contains more concordance information than $\tau$, $\nu$, ${\nu }^{\prime }\phantom{\rule{0.3em}{0ex}}$, ${\nu }^{+}$ and ${\nu }^{{+}^{\prime }}$.

Keywords
knot theory, concordance, Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R58