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Hyperbolic Knot Theory

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dc.contributor.advisor KALELKAR, TEJAS en_US
dc.contributor.author RAGHUNATH, SRIRAM en_US
dc.date.accessioned 2020-06-15T07:18:58Z
dc.date.available 2020-06-15T07:18:58Z
dc.date.issued 2020-04 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/4707
dc.description.abstract In this thesis, we study Thurston’s approach to finding complete hyperbolic structures on 3-manifolds using ideal triangulations. This approach involves solving a set of equations called the Thurston’s gluing equations. These equations are nonlinear and difficult to solve, so Casson and Rivin developed the method of angle structures through which they separated Thurston’s equations into a linear and a non-linear part and extracted geometric information from each part separately. We also study geometric triangulations of constant curvature manifolds and how they are related by Pachner moves. We specially focus on understanding geometric ideal triangulations of cusped hyperbolic 3-manifolds and prove that any two geometric ideal triangulations have a common geometric subdivision with a finite number of polytopes. As a result, geometric ideal triangulations of a cusped hyperbolic 3-manifold become related by geometric Pachner moves. Along the way, we will discuss some foundational results in the theory of 3-manifolds, triangulations and hyperbolic geometry which we require for studying the central topics in this thesis. en_US
dc.language.iso en en_US
dc.subject Low Dimensional Topology en_US
dc.subject Hyperbolic Geometry en_US
dc.subject Triangulations en_US
dc.subject 2020 en_US
dc.title Hyperbolic Knot Theory en_US
dc.type Thesis en_US
dc.type.degree BS-MS en_US
dc.contributor.department Dept. of Mathematics en_US
dc.contributor.registration 20151036 en_US


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  • MS THESES [1705]
    Thesis submitted to IISER Pune in partial fulfilment of the requirements for the BS-MS Dual Degree Programme/MSc. Programme/MS-Exit Programme

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