Name Hye Jin Jang POSTECH Session Jan 10 16:50~17:10 E11-101 New filtrations on homology cylinder group Two homology cylinders $M$ and $N$ are homology cobordant if and only if there is a 4-manifold $W$ bounding $M \cup N$ and $H_i(W,M)=H_i(W,N)=0$ for $i=1,2$. By mollifying the $H_2$ condition, we can define two coarser equivalence relations on the set of homology cylinders than homology cobordism, namely "height (h) Whitney tower cobordism" and "(h)-solvable cobordism". We investigate the nontriviality of the filtrations using $L2$-signature invariants 101-1-10/EAS8th.pdf