Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01cr56n392d
 Title: On (1,1)-knots and L-space conjecture Authors: Nie, Zipei Advisors: Szabó, Zoltán Contributors: Mathematics Department Keywords: (1,1)-knots1 bridge braidsHeegaard Floer homologyL-space conjectureleft orderable groups Subjects: Mathematics Issue Date: 2020 Publisher: Princeton, NJ : Princeton University Abstract: In this thesis, we present some results about $(1,1)$-knots and L-space conjecture. In particular, we prove that (1) L-space twisted torus knots of form $T_{p,kp\pm 1}^{l,m}$ are closures of $1$-bridge braids; (2) the L-space conjecture holds for the L-spaces obtained from Dehn surgery on closures of iterated $1$-bridge braids, and for $3$-manifolds obtained from Dehn fillings on the hyperbolic $\mathbf{Q}$-homology solid torus $v2503$; (3) there are infinitely many $(1,1)$-knots which are topologically slice but not smoothly slice. URI: http://arks.princeton.edu/ark:/88435/dsp01cr56n392d Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics