Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
Mapping class group
Summary
In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space.
Motivation
Consider a topological space, that is, a space with some notion of closeness between points in the space. We can consider the set of homeomorphisms from the space into itself, that is, continuous maps with continuous inverses: functions which stretch and deform the space continuously without breaking or gluing the space. This set of homeomorphisms can be thought of as a space itself. It forms a group under functional composition. We can also define a topology on this new space of homeomorphisms. The open sets of this new function space will be made up of sets of functions that map compact subsets K into open subsets U as K and U range throughout our original topological space, completed with their finite intersections (whic
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications
Loading
Related people
Loading
Related units
Loading
Related concepts
Loading
Related courses
Loading
Related lectures
Loading