Genus function
Genus function

Artem Kotelskiy , Princeton University
Fine Hall 314
In this talk we will see how gauge theory helps to compute minimal genus function for second homology classes inside 4manifolds. Based on adjunction inequality and Thom's generalised theorem, we will compute this function for CP^2#(CP^2), CP^1xCP^1, T^4 and CP^2. Afterwards we will examine case the of CP^2 more closely (it was Thom's conjecture for a while, stating that (d1)(d2)/2 is minimal genus for class representing d times generator of second homology of CP^2).