Levin-Wen models are microscopic spin models for topological phases of matter in （2＋ 1）-dimension. We introduce a generalization of such models to （3 ＋ 1）-dimension based on unitary braided fusion categories, al...Levin-Wen models are microscopic spin models for topological phases of matter in （2＋ 1）-dimension. We introduce a generalization of such models to （3 ＋ 1）-dimension based on unitary braided fusion categories, also known as unitary premodular categories. We discuss the ground state degeneracy on 3-manifolds and statistics of excitations which include both points and defect loops. Potential con- nections with recently proposed fractional topological insulators and projective ribbon permutation statistics are described.展开更多
Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P（-n,-m, m）. The computations reveal that the ...Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P（-n,-m, m）. The computations reveal that the rank of the homology of pretzel knots is an invariant of n. The proof is based on a ＂shortcut＂ and two lemmas that recursively reduce the computational complexity of Khovanov type homology.展开更多
We study a Khovanov type homology close to the original Khovanov homology theory from Frobenius system.The homology is an invariant for oriented links up to isotopy by applying a tautological functor on the geometric ...We study a Khovanov type homology close to the original Khovanov homology theory from Frobenius system.The homology is an invariant for oriented links up to isotopy by applying a tautological functor on the geometric complex.The homology has also geometric descriptions by introducing the genus generating operations.We prove that Jones Polynomial is equal to a suitable Euler characteristic of the homology groups.As an application,we compute the homology groups of（2,k）-torus knots for every k ∈ N.展开更多
文摘Levin-Wen models are microscopic spin models for topological phases of matter in （2＋ 1）-dimension. We introduce a generalization of such models to （3 ＋ 1）-dimension based on unitary braided fusion categories, also known as unitary premodular categories. We discuss the ground state degeneracy on 3-manifolds and statistics of excitations which include both points and defect loops. Potential con- nections with recently proposed fractional topological insulators and projective ribbon permutation statistics are described.
基金The NSF(11271282,11371013)of Chinathe Graduate Innovation Fund of USTS
文摘Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P（-n,-m, m）. The computations reveal that the rank of the homology of pretzel knots is an invariant of n. The proof is based on a ＂shortcut＂ and two lemmas that recursively reduce the computational complexity of Khovanov type homology.
基金Supported by NSFC(Grant Nos.11329101 and 11431009)
文摘We study a Khovanov type homology close to the original Khovanov homology theory from Frobenius system.The homology is an invariant for oriented links up to isotopy by applying a tautological functor on the geometric complex.The homology has also geometric descriptions by introducing the genus generating operations.We prove that Jones Polynomial is equal to a suitable Euler characteristic of the homology groups.As an application,we compute the homology groups of（2,k）-torus knots for every k ∈ N.
