2025/03/26 by Pansu, Pierre
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.20335
The aim of homotopy theory in topology is to simplify, after continuous deformation, continuous maps between topological spaces. What prevents this from happening are homotopy invariants. This raises quantitative questions: \bullet Is the calculation of invariants possible (decidable)? If so, at what cost? \bullet Is it possible to construct low-complexity representatives whose invariant values are prescribed? If so, at what cost? \bullet How complex are the necessary deformations? The answers, often recent, are extremely varied. Moreover, many questions remain open, showing that topology has not said its last word, even in low dimensions.