17 citations · 52 across the 15 of their papers we have counts for
16 papers
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…
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…
Khovanov homology detects the Hopf links
John A. Baldwin, Steven Sivek, Yi Xie
We prove that any link in whose Khovanov homology is the same as that of a Hopf link must be isotopic to that Hopf link. This holds for both reduced and unreduced Khovanov ho…
Earrings, sutures and pointed links
Yi Xie
We prove a rank inequality on the instanton knot homology and the Khovanov homology of a link in . The key step of the proof is to construct a spectral sequence relating Baldw…
sl(3) Khovanov module and the detection of the planar theta-graph
Yi Xie
We introduce two invariants called sl(3) Khovanov module and pointed sl(3) Khovanov homology for spatial webs (bipartite trivalent graphs). Those invariants are related to Kronheim…
Instantons and Annular Khovanov Homology
Yi Xie
In this paper, we introduce the annular instanton Floer homology which is defined for links in a thickened annulus. It is an analogue of the annular Khovanov homology. A spectral s…
Surgery, Polygons and -Floer Homology
Lucas Culler, Aliakbar Daemi, Yi Xie
Surgery exact triangles in various 3-manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles…
Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles
Aliakbar Daemi, Yi Xie
For each integer , Mariño and Moore defined generalized Donaldson invariants by the methods of quantum field theory, and made predictions about the values of these invaria…