MARC details
| 000 -LEADER |
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| fixed length control field |
01978nam a22002657a 4500 |
| 001 - CONTROL NUMBER |
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| control field |
th617 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20250220151923.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
250219b |||||||| |||| 00| 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| Language of cataloging |
English |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Edition number |
23rd |
| Classification number |
514.24 |
| Item number |
R888 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Roy, Biman |
| Relator term |
author |
| 245 10 - TITLE STATEMENT |
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| Title |
A1-homotopy types of A2 and A2 \ {(0, 0)}/ |
| Statement of responsibility, etc |
Biman Roy |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Kolkata: |
| Name of publisher, distributor, etc |
Indian Statistical Institute, |
| Date of publication, distribution, etc |
2024 |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
vii, 114 pages, |
| 502 ## - DISSERTATION NOTE |
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| Dissertation note |
Thesis (Ph.D) - Indian Statistical Institute, 2024 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliography |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Introduction -- A1-homotopy theory: An Introduction -- A1-invariance of πA1/ 0 (−) -- Birational Connected Components -- Existence of A1 and A1-Connectedness of a Surface -- A1-homotopy theory and log-uniruledness -- Kan Fibrant Property of Sing∗(X)(−) -- Characterisation of the Affine Space -- A1-homotopy type of A2 \ {(0, 0)} -- Regular Functions on S(X) -- Naive 0-th A1-homology -- |
| 508 ## - CREATION/PRODUCTION CREDITS NOTE |
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| Creation/production credits note |
Guided by Prof. Utsav Choudhury |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
Morel-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)}. |
| 650 #4 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics |
| 650 #4 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Homotopy |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://hdl.handle.net/10263/7485">http://hdl.handle.net/10263/7485</a> |
| Link text |
Full text |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
THESIS |
