7 papers
The Dax isomorphism for topological -manifolds
Jianfeng Lin, Yi Xie, Boyu Zhang
Let be an oriented topological -manifold with boundary. We establish a Dax isomorphism for the fundamental group of the space of embedded arcs in . Here, the embedding sp…
Splitting spheres for -links in
Jianfeng Lin, Yi Xie, Boyu Zhang
We prove that every smooth two-component split sphere link admits infinitely many smooth splitting -spheres that are topologically non-isotopic. This gene…
Topological symplectic manifolds and bi-Lipschitz structures
Dan Cristofaro-Gardiner, Boyu Zhang
We show that a topological symplectic manifold has a canonically associated bi-Lipschitz structure. As a corollary, we obtain the first examples of non-existence and non-uniqueness…
Pseudo-isotopies of 3-manifolds with infinite fundamental groups
Jianfeng Lin, Yi Xie, Boyu Zhang
Suppose is a compact, connected, oriented 3-manifold possibly with boundary, such that is infinite. Let denote the group of s…
On the mapping class groups of 4-manifolds with 1-handles
Jianfeng Lin, Yi Xie, Boyu Zhang
We develop a framework that generalizes Budney-Gabai's invariant on to 4-manifolds with 1-handles. As applications, we show that if…
Dax invariants, light bulbs, and isotopies of symplectic structures
Jianfeng Lin, Weiwei Wu, Yi Xie +1
This paper addresses several isotopy problems on -manifolds. First, we classify the isotopy classes of embeddings of in that are geometrically dual to $\{\mbox…
Z/2 harmonic 1-forms, R-trees, and the Morgan-Shalen compactification
Siqi He, Richard Wentworth, Boyu Zhang
This paper studies the relationship between an analytic compactification of the moduli space of flat connections on a closed, oriented 3-manifold de…