In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic ... Stable homotopy theory · Chromatic homotopy theory · Simple homotopy theory

1 февр. 2024 г. · Homotopy theory is the study of mathematical contexts in which functions or rather (homo-)morphisms are equipped with a concept of homotopy between them.

14 янв. 2016 г. · Persistent homology works by considering all possible covers of your dataset by balls of radius r drawn around the data points, as r varies. Roadmap for Algebraic Geometry/Homotopy Theory/Algebraic $K Homotopy theory and algebraic topology last 10 years. Is it a ... Timeline of "foundational" advances in homotopy theory? Другие результаты с сайта mathoverflow.net

20 февр. 2023 г. · Homotopy theory serves as a foundation for much of modern (higher) category theory. For instance, the proof of equivalence of various models of ...

A 1 homotopy theory or motivic homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more ...

17 февр. 2023 г. · As applications, we obtain various refinements of the homotopy groups, sensitive to the complex structure.

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic ...

Unstable homotopy theory is about understanding the detailed structure and properties of topological spaces and morphisms between them. Central to this study is ...

Equivariant techniques have played a critical role in the proofs of several major results and developments in algebraic topology over the past decade.

30 окт. 2001 г. · In this paper we develop homotopy theoretical methods for studying diagrams. In particular we explain how to construct homotopy colimits and limits in an ...