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Course# MATH-323: Algebraic topology

Summary

Homology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its properties and learn how to compute it. There will be many examples and applications.

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Instructors (1)

Related concepts (82)

Homology (mathematics)

In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology gro

Sphere

A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point

Simplicial homology

In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of a given dimension in the complex. This generaliz

Singular homology

In algebraic topology, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups H_n(X). Intuitively, singul

Simplicial complex

In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their n-dimensional counterparts (see illustration). Simplicial complexes should not be confused with

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Lectures in this course (57)