Please use this identifier to cite or link to this item: http://hdl.handle.net/10263/7485
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dc.contributor.authorRoy, Biman-
dc.date.accessioned2024-12-27T11:05:49Z-
dc.date.available2024-12-27T11:05:49Z-
dc.date.issued2024-12-
dc.identifier.citation123p.en_US
dc.identifier.urihttp://hdl.handle.net/10263/7485-
dc.descriptionThis thesis is under the supervision of Dr.Utsav Choudhuryen_US
dc.description.abstractMorel-Voevodsky developed A^1-homotopy theory which is a bridge between algebraic geometry and algebraic topology. In this thesis we study the A^1-connected component of a smooth variety in great detail. We have shown that the A^1-connected component of a smooth variety contains the information about the existence of affine lines in the variety. Using this and Miyanishi-Sugie's algebraic characterisation, we determine that the affine plane is the only A^1-contractible smooth affine surface over the field of characteristic zero. In the other part of the thesis, we studied the A^1-homotopy type of A^2-{(0,0)}. We showed that over the field of characteristic zero, if an open subvariety of a smooth affine surface is A^1-weakly equivalent to A^2-{(0,0)}, then it is isomorphic to A^2-{(0,0)}.en_US
dc.language.isoenen_US
dc.publisherIndian Statistical Institute, Kolkataen_US
dc.relation.ispartofseriesISI Ph. D Thesis;TH-
dc.subjectA^1-homotopy theoryen_US
dc.subjectAffine algebraic geometryen_US
dc.subjectZariski Cancellationen_US
dc.titleA1-homotopy types of A2 and A2 \ {(0, 0)}en_US
dc.typeThesisen_US
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