QUALIFYING EXAMINATION Harvard University Department of Mathematics Tuesday, March 12 (DayLet X be a compact n-dimensional differentiable manifold, and Y ⊂ X a closed submanifold of dimension m. Show that the E

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161 Documenta Math. Sobolev Spaces on Lie Manifolds and Regularity for Polyhedral Domains

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• Mathematical analysis
• Mathematics
• Algebra
• Sobolev spaces
• Differential forms
• Connection
• Integration on manifolds
• Manifolds
• Differentiable manifold
• Volume form
• Topological manifold
• Vector space

161 Documenta Math. Sobolev Spaces on Lie Manifolds and Regularity for Polyhedral Domains

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• Mathematical analysis
• Mathematics
• Algebra
• Sobolev spaces
• Differential forms
• Connection
• Integration on manifolds
• Manifolds
• Differentiable manifold
• Volume form
• Topological manifold
• Vector space

On the geometry of polar varieties 1 B. Bank 2 , M. Giusti 3 , J. Heintz 4 , M. Safey El Din 5 , E. Schost 6 November 21, 2009 Abstract

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• Abstract algebra
• Algebra
• Mathematics
• Algebraic geometry
• Smooth scheme
• Zariski topology
• Local ring
• Algebraic variety
• Differentiable manifold
• Affine variety
• CW complex

arXiv:0801.4345v2 [math.DG] 26 FebLimit leaves of a CMC lamination are stable William H. Meeks III∗ Joaqu´ın P´erez

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• Mathematical analysis
• Curvature
• Mathematics
• Riemannian geometry
• Geometry
• 3-manifold
• Geometric topology
• Differential geometry of surfaces
• Holonomy
• Limit of a function
• Riemannian manifold
• Differentiable manifold

Geometry/Topology ˆ The A-genus of S 1-manifolds with finite second homotopy group Manuel Amann a,1 , Anand Dessai b,2

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• Topology
• Geometric topology
• Mathematical physics
• Genus of a multiplicative sequence
• Signature
• Differentiable manifold
• Diffeomorphism
• Surgery theory
• Manifolds

Cosymplectic p-spheres Beniamino Cappelletti-Montano, Antonio De Nicola, and Ivan Yudin (full paper available in ArXiv:Abstract We introduce cosymplectic circles and cosymplectic spheres and classify compact 3

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• Differential topology
• Topology
• Differential geometry
• Symplectic geometry
• Smooth manifolds
• Riemannian geometry
• Sasakian manifold
• Geometric topology
• Contact geometry
• Almost complex manifold
• Differentiable manifold
• Symplectic manifold

2. PROBLEM SET FOR “DIFFERENTIAL GEOMETRY II” AKA “ANALYSIS AND GEOMETRY ON MANIFOLDS” WINTER TERMProblem 4. Prove the following theorem from class, which defines the product of smooth manifolds.

Source URL: carsten.codimi.de

• Topology
• Mathematics
• Mathematical analysis
• Geometric topology
• Differentiable manifold
• Smooth structure
• Manifolds
• Handle decomposition
• Complex manifold

Directional Field Synthesis, Design, and Processing

Source URL: www.cs.technion.ac.il

• Mathematics
• Algebra
• Mathematical analysis
• Differential geometry
• Differential topology
• Vector calculus
• Connection
• Vectors
• Vector
• Curl
• Tangent space
• Differentiable manifold

“THE HOMOTOPY TYPE OF THE COBORDISM CATEGORY” PROPOSAL FOR A SEMINAR PROGRAM WINTERSEMESTERThe main aim of the seminar will be to understand the main theorem in [GMTW07] and its proof.

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• Topology
• Abstract algebra
• Algebra
• Algebraic topology
• Surgery theory
• Homotopy theory
• Differential topology
• Sheaf theory
• Sheaf
• Cobordism
• Differentiable manifold
• H-cobordism