# Geometric topology

In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. (Wikipedia).  Topology (What is a Topology?)

What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b

From playlist Topology What is the definition of a geometric sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences Topology 1.4 : Product Topology Introduction

In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology How to determine the rule for a geometric sequence given two values

👉 Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi

From playlist Sequences Topology 1.1 : Open Sets of Reals

In this video, I give a definition of the open sets on the real numbers. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology What is a geometric mean

Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.

From playlist Geometry - GEOMETRIC MEAN Learn how to determine the sum of a geometric finite series

👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term

From playlist Series Evaluating the partial sum of a geometric series

👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term

From playlist Series What is a closed set ?

I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla

From playlist Topology Jessica Purcell - Lecture 3 - Knots in infinite volume 3-manifolds

Jessica Purcell, Monash University Title: Knots in infinite volume 3-manifolds Classically, knots have been studied in the 3-sphere. However, many examples of knots arising in applications lie in broader classes of 3-manifolds. These include virtual knots, which lie within thickened surfa Laurent Lafforgue - 3/4 Classifying toposes of geometric theories

Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose

From playlist Toposes online Geometry of Surface Group Representations by Mahan Mj

ICTS at Ten ORGANIZERS: Rajesh Gopakumar and Spenta R. Wadia DATE: 04 January 2018 to 06 January 2018 VENUE: International Centre for Theoretical Sciences, Bengaluru This is the tenth year of ICTS-TIFR since it came into existence on 2nd August 2007. ICTS has now grown to have more tha

From playlist ICTS at Ten Ulysses Alvarez - The Up Topology on the Grassmann Poset

38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Ulysses Alvarez, Binghamton University Title: The Up Topology on the Grassmann Poset Abstract: For a discrete poset X, McCord proved that there exists a weak homotopy equivalence from the order complex |X| to where X has Laurent Lafforgue - 1/4 Classifying toposes of geometric theories

Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose

From playlist Toposes online Jens Hemelaer - Toposes of presheaves on monoids as generalized topological spaces

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/HemelaerSlidesToposesOnline.pdf Various ideas from topology have been generalized to toposes, for example surjection

From playlist Toposes online Johnathan Bush (11/5/21): Maps of Čech and Vietoris–Rips complexes into euclidean spaces

We say a continuous injective map from a topological space to k-dimensional euclidean space is simplex-preserving if the image of each set of at most k+1 distinct points is affinely independent. We will describe how simplex-preserving maps can be useful in the study of Čech and Vietoris–Ri

From playlist Vietoris-Rips Seminar Nuances of Topological Superconductivity in Sr intercalated Bi2Se3 and Exceptional... by S. Patnaik

DISCUSSION MEETING : GEOMETRIC PHASES IN OPTICS AND TOPOLOGICAL MATTER ORGANIZERS : Subhro Bhattacharjee, Joseph Samuel and Supurna Sinha DATE : 21 January 2020 to 24 January 2020 VENUE : Madhava Lecture Hall, ICTS, Bangalore This is a joint ICTS-RRI Discussion Meeting on the geometric Topology 1.6 : Metric Topology

In this video, I introduce the metric topology, and introduce how the topologies it generates align with the standard topologies on Euclidean space. Email : fematikaqna@gmail.com Subreddit : https://www.reddit.com/r/fematika Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology Topology of Random Geometric Complexes in High-Dimensions by Akshay Goel

ICTS In-house 2022 Organizers: Chandramouli, Omkar, Priyadarshi, Tuneer Date and Time: 20th to 22nd April, 2022 Venue: Ramanujan Hall inhouse@icts.res.in An exclusive three-day event to exchange ideas and research topics amongst members of ICTS.

From playlist ICTS In-house 2022