Goeritz Groups of Genus Two and Genus Three Heegaard Splitting of the Three Sphere

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dc.contributor.authorPanda, Swapnendu
dc.date.accessioned2022-11-01T11:37:46Z
dc.date.accessioned2023-10-20T12:31:07Z
dc.date.available2022-11-01T11:37:46Z
dc.date.available2023-10-20T12:31:07Z
dc.date.issued2021
dc.descriptionSupervisor: Palaparthi, Sree Krishna Anantha Saien_US
dc.description.abstractIn this work, we present a finite generating set (j2 of J-li, the genus-2 Goeritz group of S3, in terms of Dehn twists about certain simple closed curves on the standard Heegaard surface. We present an algorithm that describes an element f EJ-12 as a word in the alphabet of (j 2 in a certain format. Using a complexity measure defined on reducing spheres, we show that such a description off eJ-li is unique. We also present a finite subset (j3 of Jf3, the genus-3 Goeritz group of S3. We show that the elements in (h generates the generating elements of J{j proposed by Freedman and Scharlemann. Thus, we verify that (j 3 is a generating set of_J-6en_US
dc.identifier.otherROLL NO.126123003
dc.identifier.urihttps://gyan.iitg.ac.in/handle/123456789/2200
dc.language.isoenen_US
dc.relation.ispartofseriesTH-2740;
dc.subjectGoeritz Groupsen_US
dc.subjectHeegaard Splittingen_US
dc.subjectThree Sphereen_US
dc.titleGoeritz Groups of Genus Two and Genus Three Heegaard Splitting of the Three Sphereen_US
dc.typeThesisen_US
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