Lathisms Lecture: Loops and Homotopy
Автор: LATHISMS
Загружено: 2025-05-05
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Lathisms Lecture: Loops and Homotopy
Lathisms Lecture: Loops and Homotopy
Register for our June 6, at 3 PM EST event where we will discuss this lecture at http://tinyurl.com/Lathisms2024-25
Speaker: Sofía Martínez Alberga
Abstract: To any based topological space, (X,b), we can associate it to another based topological space known as the loop space, (Ω_b(X), c). The elements of the loop space are functions from the unit interval, [0,1], to the based topological space, (X,b), where the images of 0 and 1 are , and in practice these functions are called loops! This talk will discuss the algebraic structure that the loop space is hiding and what said structure they can encode. For example, one can define a product of loops and ask if commutativity and associativity are satisfied. By the end of this talk, we will consider topological spaces with an action of the group and compare such spaces by means of its fundamental group.
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