Moderately Discontinuous Algebraic Topology - An Introduction to Metric Invariants

Explore a lecture on Moderately Discontinuous Homology and Homotopy, a new metric algebraic topology theory, presented by Maria Pe Pereira from Universidad Complutense de Madrid. Discover how this mathematical framework provides invariants for germs that are topologically cones in R^n and continuous families of sets in R^n x R. Learn how the theory captures bilipschitz information and quasi isometric invariants by examining sets with metric structures derived from euclidean or riemannian metrics. Understand how the theory analyzes different speeds of topological collapse in cone structures relative to the origin, and similar collapsing behaviors in degenerating families relative to family parameters. Gain insights into the theory's original context and its potential expansion into broader applications through this gentle introduction to the mathematical concepts.