Vector bundle

Results: 342



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181Algebraic topology / Algebraic geometry / Homotopy theory / Projective geometry / Differential topology / Grassmannian / Algebraic K-theory / K-theory / Vector bundle / Abstract algebra / Topology / Algebra

Contents[removed]January 3: Gersten’s conjecture: If A is a discrete valuation ring with residue field k, then the transfer map K∗ (k) → K∗ (A) is zero. January 6: Exact categories with a resolving full exact

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Source URL: www.claymath.org

Language: English - Date: 2014-04-29 09:27:06
182Connection / Fiber bundles / Differential topology / Vector bundles / Connection form / Parallel transport / Vector space / Vector-valued differential form / Frame bundle / Topology / Algebra / Differential geometry

Week 5 (due Feb[removed]Let E be a real vector bundle of rank r with a connection ∇. Let ω be the corresponding connection 1-form defined on some trivializing neighborhood U . As explained in class, ∇ enables us to

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Source URL: www.theory.caltech.edu

Language: English - Date: 2009-02-05 13:39:31
183Algebraic topology / Differential topology / Characteristic classes / Homotopy theory / Chern class / Line bundle / Vector bundle / Stiefel–Whitney class / Circle bundle / Topology / Abstract algebra / Mathematics

Week 1 (due April[removed]As was explained during the winter quarter, to any line bundle (complex vector bundle of rank one) on a manifold M one can associate its first Chern class which takes values in H 2 (M, Z), and two

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Source URL: www.theory.caltech.edu

Language: English - Date: 2009-04-01 22:32:01
184Moduli theory / Vector bundles / Invariant theory / Differential topology / Moduli space / Moduli of algebraic curves / Michael Atiyah / Geometric invariant theory / Ample line bundle / Abstract algebra / Algebraic geometry / Topology

Clay Mathematics Proceedings Volume 14 Grassmannians, Moduli Spaces and Vector Bundles Clay Mathematics Institute Workshop

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Source URL: www2.maths.ox.ac.uk

Language: English - Date: 2013-12-04 05:55:00
185Mathematics / Algebraic topology / Differential geometry / Characteristic classes / Fiber bundles / Chern class / Vector bundle / Connection form / Connection / Topology / Abstract algebra / Differential topology

Week 4 (due April[removed]The Todd genus is the Chern genus corresponding to the analytic function f (z) = z/(ez − 1). Express the Todd genus in terms of Chern classes up to and including terms of cohomological degree 6

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Source URL: www.theory.caltech.edu

Language: English - Date: 2009-04-23 15:07:06
186Connection / Differential topology / Fiber bundles / Vector bundles / Connection form / Curvature / Tangent bundle / Spherical coordinate system / Frame bundle / Topology / Mathematical analysis / Differential geometry

Week 6 (due Feb[removed]Problem 6.8 in Morita. 2. Consider a unit sphere S 2 in R3 . The tangent bundle to R3 is trivial and one can define a connection on it by letting ∇

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Source URL: www.theory.caltech.edu

Language: English - Date: 2009-02-12 15:45:18
187Abstract algebra / Fiber bundles / Differential topology / Connection / Group actions / Principal bundle / Vector bundle / Normal distribution / Hilbert scheme / Topology / Differential geometry / Mathematical analysis

Proc. Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 3, August 2014, pp. 315–332. c Indian Academy of Sciences  Schematic Harder–Narasimhan stratification for families of principal bundles and -modules

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Source URL: www.ias.ac.in

Language: English - Date: 2014-08-22 07:31:23
188Differential geometry / Connection / Differential topology / Fiber bundles / Linear algebra / Almost complex manifold / Riemannian manifold / Vector space / Lie derivative / Algebra / Mathematical analysis / Mathematics

Proc. Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 3, August 2014, pp. 427–436. c Indian Academy of Sciences  Geometry of the cotangent bundle with Sasakian metrics and its applications

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Source URL: www.ias.ac.in

Language: English - Date: 2014-08-22 07:31:29
189Algebraic topology / Group theory / Vectors / Projective geometry / K-theory / Grassmannian / Topological K-theory / Elliptic curve / Vector bundle / Algebra / Abstract algebra / Mathematics

Contents[removed]January 1974: The stability problem for GL(k), k = Fq . January 3: Stability proofs. January 4: 2-planes and bouquets of spheres. January 6, 7: More stability.

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Source URL: www.claymath.org

Language: English - Date: 2014-04-29 09:28:25
190Abstract algebra / Differential topology / Vector bundles / Algebraic geometry / Analytic geometry / Tangent space / Tangent bundle / Differentiable manifold / Curve / Geometry / Topology / Differential geometry

Math. Ann. 256, [removed]Am 9 Springer-Verlag 1981

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Source URL: www.msri.org

Language: English - Date: 2005-09-16 12:56:35
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