# A Guide to the Classification Theorem for Compact Surfaces

A Guide to the Classification Theorem for Compact Surfaces is a textbook in topology, on the classification of two-dimensional surfaces. It was written by Jean Gallier and Dianna Xu, and published in 2013 by Springer-Verlag as volume 9 of their Geometry and Computing series (doi:10.1007/978-3-642-34364-3, ISBN 978-3-642-34363-6). The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. (Wikipedia).

Math 131 092116 Properties of Compact Sets

Properties of compact sets. Compact implies closed; closed subsets of compact sets are compact; collections of compact sets that satisfy the finite intersection property have a nonempty intersection; infinite subsets of compact sets must have a limit point; the infinite intersection of ne

Math 101 Fall 2017 112917 Introduction to Compact Sets

Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi

From playlist Course 6: Introduction to Analysis (Fall 2017)

Math 101 Introduction to Analysis 112515: Introduction to Compact Sets

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From playlist Course 6: Introduction to Analysis

Complex surfaces 1: Introduction

This talk is part of a series giving an informal survey of complex algebraic surfaces. We give an overview of the Enriques-Kodaira classification, with examples of most of the different types of surfaces. We conclude by giving an example of a non-algebraic surface: the Hopf surface. Furth

From playlist Algebraic geometry: extra topics

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This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a quick review of category theory as background for the definition of morphisms of algebraic varieties.

From playlist Algebraic geometry I: Varieties

Alexandre Sukhov - J-complex curves: some applications (Part 4)

We will focus in our lectures on the following : 1. J-complex discs in almost complex manifolds : general properties. Linearization and compactness. Gromov’s method : the Fredholm alternative for the d-bar operator. Attaching a complex disc to a Lagrangian manifold. Application : exotic sy

Growth of cohomology in towers of manifolds: a topological applica... - Mathilde Gerbelli-Gauthier

Members’ Colloquium Topic: Growth of cohomology in towers of manifolds: a topological application of the Langlands program Speaker: Mathilde Gerbelli-Gauthier Affiliation: Member, School of Mathematics Date: November 15, 2021 How does the dimension of the first cohomology grow in a tower

From playlist Mathematics

Brent Pym: Holomorphic Poisson structures - lecture 3

The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a cano

From playlist Virtual Conference

The Computational Complexity of Geometric Topology Problems - Greg Kuperberg

Greg Kuperberg University of California, Davis September 24, 2012 This talk will be a partial survey of the first questions in the complexity theory of geometric topology problems. What is the complexity, or what are known complexity bounds, for distinguishing n-manifolds for various n? Fo

From playlist Mathematics

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From playlist Algebraic geometry: extra topics

Antoine Song - Spherical Plateau problem and applications

I will discuss an area minimization problem in certain quotients of the Hilbert sphere by countable groups. An early version of that setting appears in Besson-Courtois-Gallot’s work on the entropy inequality. As an application of this minimization problem, we obtain some stability results.

From playlist Not Only Scalar Curvature Seminar

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The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the secon

Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings

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This is the fourth of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lecture covers connected sums, orientations, and finally the classificatio

Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology

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From playlist Ian Agol: 24th Workshop in Geometric Topology

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From playlist Functions (Discrete Math)

Dynamics on character varieties - William Goldman

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From playlist Mathematics

Alexandre Sukhov - J-complex curves: some applications (Part 1)

We will focus in our lectures on the following : 1. J-complex discs in almost complex manifolds : general properties. Linearization and compactness. Gromov’s method : the Fredholm alternative for the d-bar operator. Attaching a complex disc to a Lagrangian manifold. Application : exotic sy