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Title: On (1,1)-knots and L-space conjecture
Authors: Nie, Zipei
Advisors: Szabó, Zoltán
Contributors: Mathematics Department
Keywords: (1,1)-knots
1 bridge braids
Heegaard Floer homology
L-space conjecture
left 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.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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