Codes, mapping class group and 4-manifolds generalizing the Kummer surface

Meeting ID: 916 5855 1117
Password: as before.
Contact: Aru Ray, Tobias Barthel,Viktoriya Ozornova
Slides: are attached on the Talk's page or see our Nextcloud [3]
 

The idea to offer this talk came during the mini series about constructions of 4-manifolds. It is an old story (meaning from about 15 years ago). There is a relation between 3-manifolds with an involution and binary self dual codes, which mathematically are surprisingly interesting objects with relations to modular forms etc. Being interesting indicates that they are not easy to find. For each element in the mapping class group of surfaces there is a 3-manifold with involution and so a code. Amongst the self dual codes there are better ones, the doubly even codes. One can decide topologically when such a code is doubly even by a construction of 4-manifolds which generalize the Kummer surface.  From this point of view the Kummer surface is related to the Hamming code, which is related to the E_8 lattice. There is a 4-manifold (which I don't  know explicitly) which is in a similar way related to the Leech lattice. All this will be explained.