7 papers
The dimension of Kronheimer-Mrowka instanton homology group for plane trivalent graphs
Zipei Zhuang
We proved that the dimension of the F-vector space J#(G) for a plane trivalent graph G, defined by Kronheimer and Mrowka using their SO(3) instanton Floer homology, is equal to the…
Knot cobordism and Lee's perturbation of Khovanov homology
Zipei Zhuang
For a connected cobordism S between two knots K1,K2 in S3, we establish an inequality involving the number of local maxima, the genus of S, and the torsion orders of Kht(K1),Kht(K2…
Grid homology and the unknotting number
Zipei Zhuang
We showed that the order of torsion homology classes in the grid homology of a knot is a lower bound for the unknotting number.
Tait coloring and a moduli space
ZIpei Zhuang
We associate a moduli space M(G) to a planar trivalent graph G. We proved several decomposition properties of M(G), which implies that the Euler characteristic of M(G) equals to th…
Grid homology for spatial graphs and a skein exact sequence
Zipei Zhuang
We defined a grid homology theory for spatial graphs. We showed that the skein exact sequence of singular knots can be extended to our grid homology for spatial graphs.
On the homology theory for the chromatic polynomials
Zipei Zhuang
In \cite{10.2140/agt.2005.5.1365}, Rong and Helme-Guizon defined a categorification for the chromatic polynomial of graphs , i.e. a homology theory whose Euler…