Mapping class group
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![PDF] A presentation for the mapping class group of a closed ...](/imgres?imgurl=https://d3i71xaburhd42.cloudfront.net/db1ca274ce00977afee25b1dabc739d59886dc3f/11-Figure13-1.png&imgrefurl=https://www.semanticscholar.org/paper/A-presentation-for-the-mapping-class-group-of-a-Hatcher-Thurston/db1ca274ce00977afee25b1dabc739d59886dc3f&h=1056&w=856&tbnid=ECF0NDQ6xd-U8M&q=Mapping+class+group&tbnh=150&tbnw=122&usg=AI4_-kRODmZZmw0J-lJVgUHnfJHnx6M0pA&vet=1&docid=YIGNzU1SPzeeKM&sa=X&ved=2ahUKEwivj-7zupOGAxWArYkEHS6uC8wQ9QF6BAgAEAU)
![PDF] A primer on mapping class groups | Semantic Scholar](/imgres?imgurl=https://d3i71xaburhd42.cloudfront.net/e54ba509885ee328b0e0890ec955db095f584c97/126-Figure4.5-1.png&imgrefurl=https://www.semanticscholar.org/paper/A-primer-on-mapping-class-groups-Farb-Margalit/38c7707c238e84ea606b70fc5863684b4c44852a&h=342&w=912&tbnid=5AdhjOSd3Lu8rM&q=Mapping+class+group&tbnh=55&tbnw=147&usg=AI4_-kTfs7AaTBJlPDQTPEHaocgsEv8WQg&vet=1&docid=nGdTNbQ4EDFqWM&sa=X&ved=2ahUKEwivj-7zupOGAxWArYkEHS6uC8wQ9QF6BAgAEAc)
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. Wikipedia