Monday January 27th, 2025 | |
| Time: | 12:30 PM - 1:55 PM |
| Title: | The Dehn twist on a connected sum of two homology tori |
| Speaker: | Haochen Qiu, Brandeis University |
| Location: | Math P-131 |
| Abstract: | |
| Kronheimer-Mrowka showed that the Dehn twist along a 3-sphere in the neck of the connected sum of two K3 surfaces is not smoothly isotopic to the identity. Their result requires that the manifolds are simply connected and the signature of one of them is 16 (mod 32). We generalize the Pin(2)-equivariant family Bauer-Furuta invariant to nonsimply connected manifolds, and construct a refinement of this invariant. We use it to show that, if X_1, X_2 are two homology tori such that their determinants r_1, r_2 are odd, then the Dehn twist along a 3-sphere in the neck of X_1 # X_2 is not smoothly isotopic to the identity. | |