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139897 - Introduction to Algebraic Topology through CW-complexes

Período da turma:

05/01/2026 a 16/01/2026

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Descrição:

Programa completo – ementa e referência bibliográfica:

Algebraic Topology stands as one of the most important branches of contemporary mathematics, with applications popping up in other fields like Differential Geometry, Dynamical Systems, Analysis, and Algebra. At its core, it’s about tackling topological problems using tools from algebra. While a typical course on this subject often delves into highly intricate and abstract arguments, we’ll take a slightly different route. We’ll focus on a special class of topological spaces known as CW-Complexes. For these spaces, many key results can be reached through more combinatorial arguments, which are often more intuitive and geometric. The great thing is that many important topological spaces are actually CW-complexes! For instance, the torus, wedge sums of spheres, projective spaces, compact Lie groups, and even some linear groups like SLn(R) fall into this category. One of the main points of the study of CW-complexes is the construction of the so called Classifying Space of a group G, denoted by BG, this is a topological space whose the fundamental group is isomorphic to G, such that G acts freely on KG, using this construction one can define the K-groups, the central objects of the algebraic K-theory.

Bibliografia:

A. E. Hatcher, Algebraic topology, Cambridge Univ. Press, Cambridge, 2002.

C. A. Weibel, The K-book, Graduate Studies in Mathematics, 145, Amer. Math. Soc., Providence, RI, 2013.

J. R. Munkres, Topology: a first course, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1975.

M. Artin, Algebra, Prentice Hall, Englewood Cliffs, NJ, 1991.

R. Geoghegan, Topological methods in group theory, Graduate Texts in Mathematics, 243, Springer, New York, 2008.

Carga Horária:

10 horas

Tipo:

Obrigatória

Vagas oferecidas:

100

Ministrantes:

Bruno Reis Ramos (Especialista)

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