sl(3) Khovanov module and the detection of the planar theta-graph

Yi Xie

sl(3) Khovanov module and the detection of the planar theta-graph

Geometric Topology 2018-09-14 v1

Authors: Yi Xie

Abstract

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 Kronheimer-Mrowka's instanton invariants $J^\sharp$ and $I^\sharp$ for spatial webs by two spectral sequences. As an application of the spectral sequences, we prove that sl(3) Khovanov module and pointed sl(3) Khovanov homology both detect the planar theta graph.

Keywords

sl(3) khovanov module pointed khovanov homology spatial webs spectral sequences instanton invariants planar theta graph

Cite

@article{arxiv.1809.04742,
  title  = {sl(3) Khovanov module and the detection of the planar theta-graph},
  author = {Yi Xie},
  journal= {arXiv preprint arXiv:1809.04742},
  year   = {2018}
}

Comments

33 pages, 19 figures

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