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Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Szabó, Zoltán | |
dc.contributor.author | Thakar, Ollie | |
dc.date.accessioned | 2023-07-10T14:59:31Z | - |
dc.date.available | 2023-07-10T14:59:31Z | - |
dc.date.created | 2023-04-29 | |
dc.date.issued | 2023-07-10 | - |
dc.identifier.uri | http://arks.princeton.edu/ark:/88435/dsp01x920g1113 | - |
dc.description.abstract | In this paper, we discuss the \(L\)-space conjecture, which hopes to establish a connection between the left-orderability of the fundamental group of a rational homology 3-sphere and its Heegaard Floer homology. We first present a review of Heegaard Floer homology and then a review of this conjecture itself, followed by a discussion of techniques used to solve special cases of this conjecture. We then find a new method for showing fundamental groups of certain Dehn surgeries on 2-bridge knots are left-orderable, and use this method to show that surgeries on the knot \(6_2\) with slopes in the interval \((-4, 8)\cap\mathbb{Q}\) are left-orderable. We additionally find an infinite family of 2-bridge knots for which surgeries with slopes in the interval \((-4, 4)\cap\mathbb{Q}\) are left-orderable. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.title | Heegaard Floer Homology, The \(L\)-Space Conjecture, and Left-Orderable Surgeries on 2-Bridge Knots | |
dc.type | Princeton University Senior Theses | |
pu.date.classyear | 2023 | |
pu.department | Mathematics | |
pu.pdf.coverpage | SeniorThesisCoverPage | |
pu.contributor.authorid | 920228026 | |
pu.certificate | ||
pu.mudd.walkin | No | |
Appears in Collections: | Mathematics, 1934-2024 |
Files in This Item:
File | Description | Size | Format | |
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THAKAR-OLLIE-THESIS.pdf | 550.4 kB | Adobe PDF | Request a copy |
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