{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Real rational curves of low degree","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76391"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"In the first part of the talk we will consider real planar rational curves of degree 4. We will prove that the rigid isotopy classification of real rational curves of degree 4 in the projective plane can be solved by considering their chord diagrams. In the second part of the talk, we will consider real rational knots on the 3-sphere. The 3-sphere can be realized as a subvariety of the projective space of dimension 4. Real rational knots in the 3-sphere are curves in the 4-dimensional projective space that lie on the 3-sphere. We will prove a rigid isotopy classification of all real rational knots of degrees 6.  We will also prove methods of constructing examples of real rational knots of a given degree. The rigid isotopy classification of real rational knots in the projective space is known up to degree 5. We will partially extend this result by classifying real rational knots of degree 6 with four double points, in the projective space."},{"label":"dcterms.available","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.contributor","value":"Viro, Oleg"},{"label":"dcterms.creator","value":"DMello, Shane"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"56 pg."},{"label":"dcterms.format","value":"Application/PDF"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76391"},{"label":"dcterms.issued","value":"2013-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:09Z (GMT). No. of bitstreams: 1\nDMello_grad.sunysb_0771E_11599.pdf: 559114 bytes, checksum: 48532f2e2bba557959928c6d7becaf8e (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Mathematics"},{"label":"dcterms.title","value":"Real rational curves of low degree"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/21%2F65%2F37%2F21653704942054399702348725720051984720/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/21%2F65%2F37%2F21653704942054399702348725720051984720","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}