17 citations · 49 across the 16 of their papers we have counts for
13 papers · 1 filter
Ring structures in singular instanton homology
Yi Xie, Boyu Zhang
We calculate the ring structure of the singular instanton Floer homology of with C-coefficients, where is a closed oriented surface…
A deformation of Asaeda-Przytycki-Sikora homology
Zhenkun Li, Yi Xie, Boyu Zhang
We define a 1-parameter family of homology invariants for links in thickened oriented surfaces. It recovers the homology invariant of Asaeda-Przytycki-Sikora (arxiv:0409414) and th…
Instanton homology and knot detection on thickened surfaces
Zhenkun Li, Yi Xie, Boyu Zhang
Suppose is a compact oriented surface (possibly with boundary) that has genus zero, and L is a link in the interior of . We prove that the Asaeda-Przytycki-Sikor…
On Floer minimal knots in sutured manifolds
Zhenkun Li, Yi Xie, Boyu Zhang
Suppose is a balanced sutured manifold and is a rationally null-homologous knot in . It is known that the rank of the sutured Floer homology of i…
On meridian-traceless SU(2)-representations of link groups
Yi Xie, Boyu Zhang
Suppose L is a link in . We show that admits an irreducible meridian-traceless representation in SU(2) if and only if L is not the unknot, the Hopf link, or a con…
Equivariant Cerf theory and perturbative Casson invariants
Shaoyun Bai, Boyu Zhang
We develop an equivariant Cerf theory for Morse functions on finite-dimensional manifolds with group actions, and adapt the technique to the infinite-dimensional setting to study t…
Instantons and Khovanov skein homology on
Yi Xie, Boyu Zhang
Asaeda, Przytycki and Sikora defined a generalization of Khovanov homology for links in -bundles over compact surfaces. We prove that for a link , the…
Two detection results of Khovanov homology on links
Zhenkun Li, Yi Xie, Boyu Zhang
We prove that Khovanov homology with Z/2-coefficients detects the link L7n1, and the union of a trefoil and its meridian.
On links with Khovanov homology of small ranks
Yi Xie, Boyu Zhang
We classify all links whose Khovanov homology have ranks no greater than 8, and all three-component links whose Khovanov homology have ranks no greater than 12, where the coefficie…
Classification of links with Khovanov homology of minimal rank
Yi Xie, Boyu Zhang
If L is an oriented link with components, then the rank of its Khovanov homology is at least . We classify all the links whose Khovanov homology with Z/2-coefficients achi…
Instanton Floer homology for sutured manifolds with tangles
Yi Xie, Boyu Zhang
We prove an excision theorem for the singular instanton Floer homology that allows the excision surfaces to intersect the singular locus. This is an extension of the non-singular e…
Modulo 2 counting of Klein-bottle leaves in smooth taut foliations
Boyu Zhang
This article proves that the parity of the number of Klein-bottle leaves in a smooth cooriented taut foliation is invariant under smooth deformations within taut foliations, provid…
Monopoles and foliations without holonomy-invariant transverse measure
Boyu Zhang
This article proves a uniform exponential decay estimate for Seiberg-Witten equations on non-compact 4-manifolds with exact symplectic ends of bounded geometry. This is an extensio…