Good cover (algebraic topology)

Coverings of the Circle

A covering of a topological space X is a topological space Y together with a continuous surjective map from X to Y that is locally bi-continuos. The infinite spiral is for example a covering of the circle. Notice how every path on the circle can be lifted to the spiral. If a coveri

From playlist Algebraic Topology

Algebraic topology: Introduction

This lecture is part of an online course on algebraic topology. This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism). The book "algebraic topology" by Allen Hatcher men

From playlist Algebraic topology

Covering spaces | Algebraic Topology | NJ Wildberger

We introduce covering spaces of a space B, an idea that is naturally linked to the notion of fundamental group. The lecture starts by associating to a map between spaces, a homomorphism of fundamental groups. Then we look at the basic example of a covering space: the line covering a circle

From playlist Algebraic Topology

Covering spaces and 2-oriented graphs | Algebraic Topology | NJ Wildberger

We illustrate the idea of a covering space by looking at the rich examples coming from a wedge of two circles. Coverings of this space are graphs with each vertex of degree four, with edges suitably labelled in a directed way with alpha's and beta's. We also introduce the idea of a unive

From playlist Algebraic Topology

Algebraic Topology - 5.1 - Mappings Spaces and the Compact Open Topology

We define the compact open topology on mapping spaces.

From playlist Algebraic Topology

Algebraic Topology - 9 - Topology of Pushouts and Pullbacks

From playlist Algebraic Topology

Algebraic Topology - 5.3 - Mapping Spaces and the Compact Open Topology

Description of the adjunction (X \times -, Top(X,-))

From playlist Algebraic Topology

Epic Math Book Speed Run

In this video I do a speed run of some of my math books. I go through math books covering algebra, trigonometry, calculus, advanced calculus, real analysis, abstract algebra, differential geometry, set theory, discrete math, finite math, graph theory, combinatorics, number theory, galois t

From playlist Book Reviews

AlgTopReview: An informal introduction to abstract algebra

This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is

From playlist Algebraic Topology

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the Universal Covering Group concept In this lesson we examine another amazing connection between the algebraic properties of the Lie groups with topological properties. We will lay the foundation to understand how discrete invaria

From playlist Lie Groups and Lie Algebras

AlgTop1: One-dimensional objects

This is the first lecture of this beginner's course in Algebraic Topology (after the Introduction). In it we introduce the two basic one-dimensional objects: the line and circle. The latter has quite a few different manifestations: as a usual Euclidean circle, as the projective line of one

From playlist Algebraic Topology: a beginner's course - N J Wildberger

Weil conjectures 7: What is an etale morphism?

This talk explains what etale morphisms are in algebraic geometry. We first review etale morphisms in the usual topology of complex manifolds, where they are just local homeomorphism, and explain why this does not work in algebraic geometry. We give a provisional definition of etale morphi

From playlist Algebraic geometry: extra topics

CDH methods in K-theory and Hochschild homology - Charles Weibel

Charles Weibel Rutgers University; Member, School of Mathematics November 11, 2013 This is intended to be a survey talk, accessible to a general mathematical audience. The cdh topology was created by Voevodsky to extend motivic cohomology from smooth varieties to singular varieties, assumi

From playlist Mathematics

Duality in Algebraic Geometry by Suresh Nayak

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group We are finally in position to understand the nature of the Universal Covering Group and its connection to all the Lie groups which share a single Lie algebra. This is a critical lecture! In this lecture we simply state

From playlist Lie Groups and Lie Algebras

Robert Ghrist, Lecture 3: Topology Applied III

27th Workshop in Geometric Topology, Colorado College, June 12, 2010

From playlist Robert Ghrist: 27th Workshop in Geometric Topology

Lecture 7: Sheaves of sets (Part 2)

The most important examples of topoi are categories of sheaves of sets on a small category. Patrick Eilliott introduced this class of examples over two talks, of which is the second. In this talk he defines Grothendieck topologies and the category of sheaves on a site, and develops the exa

From playlist Topos theory seminar

Peter SCHOLZE (oct 2011) - 5/6 Perfectoid Spaces and the Weight-Monodromy Conjecture

We will introduce the notion of perfectoid spaces. The theory can be seen as a kind of rigid geometry of infinite type, and the most important feature is that the theories over (deeply ramified extensions of) Q_p and over F_p((t)) are equivalent, generalizing to the relative situation a th

From playlist Peter SCHOLZE (oct 2011) - Perfectoid Spaces and the Weight-Monodromy Conjecture

Coffee Cup Donut

To a topologist, a coffee cup and a donut are the same thing.

From playlist Algebraic Topology

Reconstruction in Algebraic Geometry - Peter Haine

Spring Opportunities Workshop 2023 Topic: Reconstruction in Algebraic Geometry Speaker: Peter Haine Affiliation: IAS Date: January 12, 2023 A classical theorem of Neukirch and Uchida says that number fields are completely determined by their absolute Galois groups. One might wonder abou

From playlist Spring Opportunities Workshop 2023