\documentclass[12pt]{article}
\usepackage{amsmath,mathrsfs,bbm}
\usepackage{amssymb}
\textwidth=4.825in
\overfullrule=0pt
\thispagestyle{empty}
\begin{document}
\noindent
%
%
{\bf Kazuhiro Kawamura}
%
%
\medskip
\noindent
%
%
{\bf Independence Complexes and Edge Covering Complexes via Alexander Duality}
%
%
\vskip 5mm
\noindent
%
%
%
%
The combinatorial \,Alexander dual\, of the independence complex
$\mathrm{Ind}(G)$ and that of the edge covering complex
$\mathrm{EC}(G)$ are shown to have isomorphic homology groups for each
non-null graph $G$. This yields isomorphisms of homology groups of
$\mathrm{Ind}(G)$ and $\mathrm{EC}(G)$ with homology dimensions being
appropriately shifted and restricted. The results exhibits the
complementary nature of homology groups of $\mathrm{Ind}(G)$ and
$\mathrm{EC}(G)$ which had been proved by Ehrenborg-Hetyei,
Engstr{\"o}m, and Marietti-Testa for forests at homotopy level.
\end{document}