Topology/Geometry Jan 2012

... (b) Define a local coordinate system on M and compute the Riemannian metric induced on M by its embedding into Euclidean R3 in terms of these local coordinates. ...

... (b) Define a local coordinate system on M and compute the Riemannian metric induced on M by its embedding into Euclidean R3 in terms of these local coordinates. ...

Math 130 Worksheet 2: Linear algebra

... Math 130 Worksheet 2: Linear algebra ... but I thought this was a geometry class! ...

... Math 130 Worksheet 2: Linear algebra ... but I thought this was a geometry class! ...

1300Y Geometry and Topology, Assignment 1 Exercise 1. Let Γ be a

... form a Lie group G, and that the unipotent matrices with integer entries forms a discrete subgroup Γ. Show that G/Γ is a compact smooth 3dimensional manifold, where Γ acts by left multiplication. Exercise 2. Show that the orthogonal, unitary and symplectic groups O(n, R), U (n) and Sp(2n, R) are smo ...

... form a Lie group G, and that the unipotent matrices with integer entries forms a discrete subgroup Γ. Show that G/Γ is a compact smooth 3dimensional manifold, where Γ acts by left multiplication. Exercise 2. Show that the orthogonal, unitary and symplectic groups O(n, R), U (n) and Sp(2n, R) are smo ...

LECTURE 30: INDUCED MAPS BETWEEN CLASSIFYING SPACES

... Suppose that α : G → H is a homomorphism of topological groups. We can get an induced map α∗ : BG → BH by providing a natural transformation between the functors that these spaces rep resent: α∗ : {Gbundles over X} → {Hbundles over X}. Namely, send a Gbundle E → X to the Hbundle H ×G E → X wher ...

... Suppose that α : G → H is a homomorphism of topological groups. We can get an induced map α∗ : BG → BH by providing a natural transformation between the functors that these spaces rep resent: α∗ : {Gbundles over X} → {Hbundles over X}. Namely, send a Gbundle E → X to the Hbundle H ×G E → X wher ...

Introduction: What is Noncommutative Geometry?

... • involutive algebra A with representation π : A → L(H) • self adjoint operator D on H, dense domain • compact resolvent (1 + D2)−1/2 ∈ K • [a, D] bounded ∀a ∈ A • even if Z/2- grading γ on H [γ, a] = 0, ∀a ∈ A, ...

... • involutive algebra A with representation π : A → L(H) • self adjoint operator D on H, dense domain • compact resolvent (1 + D2)−1/2 ∈ K • [a, D] bounded ∀a ∈ A • even if Z/2- grading γ on H [γ, a] = 0, ∀a ∈ A, ...

Branches of differential geometry

... Finsler geometry has the Finsler manifold as the main object of study — this is a differential manifold with a Finsler metric, i.e. a Banach norm defined on each tangent space. A Finsler metric is a much more general structure than a Riemannian metric. A Finsler structure on a manifold M is a functi ...

... Finsler geometry has the Finsler manifold as the main object of study — this is a differential manifold with a Finsler metric, i.e. a Banach norm defined on each tangent space. A Finsler metric is a much more general structure than a Riemannian metric. A Finsler structure on a manifold M is a functi ...

Program for ``Topology and Applications``

... modern language and, as example, present the full classi ication of all 3-dimensional homogeneous spaces with non-solvable transformation group. We also show that the same problem in the nilpotent case does not admit a parametrization by a inite number of independent parameters. ...

... modern language and, as example, present the full classi ication of all 3-dimensional homogeneous spaces with non-solvable transformation group. We also show that the same problem in the nilpotent case does not admit a parametrization by a inite number of independent parameters. ...