Browsing by Advisor "Gadgil, Siddhartha"
Now showing items 16 of 6

Compactness Theorems for The Spaces of Distance Measure Spaces and Riemann Surface Laminations
(20180218)Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the GromovHausdorﬀ distance, is a theorem with many applications. In this thesis, we give a ... 
Goldman Bracket : Center, Geometric Intersection Number & Length Equivalent Curves
(20171130)Goldman [Gol86] introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface F . This Lie bracket is known as the Goldman bracket ... 
Maps Between Noncompact Surfaces
This thesis focuses on studying proper maps between two noncompact surfaces with a particular emphasis on the topological rigidity and the Hopfian property. Topological rigidity is the property that every homotopy equivalence ... 
Mechanising knot Theory
(20180131)Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories ... 
Relative Symplectic Caps, Fibered Knots And 4Genus
(20140407)The 4genus of a knot in S3 is an important measure of complexity, related to the unknotting number. A fundamental result used to study the 4genus and related invariants of homology classes is the Thom conjecture, proved ... 
Shortest Length Geodesics on Closed Hyperbolic Surfaces
(20180131)Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this ...