Outline of Math 623; Topics in Geometric Topology: Manifold Theory
ثبت نشده
چکیده
The basic topic will be the classification of manifolds with a focus on surgery theory; the classification of high dimensional manifolds. I will, however, cover topics of interest to low-dimensional topologists and algebraic topologists. The prerequisites are Math 521 and 522, in other words singular homology theory, CW complexes, fundamental group, and covering spaces. But familiarity with the cohomology ring, homotopy groups, and the definition of a differentiable manifold and its tangent bundle would help, as would some of Chapter 4 of Davis-Kirk.
منابع مشابه
Conformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
متن کاملTopics in Representation Theory: Other Topics
• Topology of G/T : Flag manifolds G/T have cohomology only in even degrees, with Euler characteristic the degree of the Weyl group. The Euler characteristic can be calculated by a Lefschetz fixed point argument (see Adams [1], pgs. 90-92 for this). Identifying the flag manifold with a co-adjoint orbit, there is a Morse theory calulation of the cohomology that goes back to Bott, for an outline ...
متن کاملOn some generalized recurrent manifolds
The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds, called, super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [A.A. Shaikh and A. Patra, On a generalized class of recurrent manifolds, Arch. Math. (Brno) 46 (2010) 71--78.] and weakly generalized recurrent manifolds ...
متن کاملA Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملGuaranteeing 2-Manifold Property for Meshes
Meshes are the most commonly used objects in computer graphics. They generalize polyhedra by using non-planar faces. Modeling 2-dimensional manifold meshes with a simple user interface is an important problem in computer aided geometric design. In this work we propose a conceptual framework for mesh modeling systems that guarantees topologically correct 2-dimensional manifolds. Our solution is ...
متن کامل