# The 4x5 chessboard complex is the complement of a link, which link?

 Importance: Medium ✭✭
 Author(s): David Eppstein
 Subject: Topology
 Keywords: knot theory, links, chessboard complex
 Recomm. for undergrads: no
 Posted by: rybu on: September 4th, 2010

\begin{problem} Ian Agol and Matthias Goerner observed that the 4x5 chessboard complex is the complement of many distinct links in the 3-sphere. Their observation is non-constructive, as it uses the resolution of the Poincare Conjecture. Find specific links that have the 4x5 chessboard complex as their complement. \end{problem}

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See the MathOverFlow thread: \href [Is the 4x5 chessboard complex a link complement?]{http://mathoverflow.net/questions/36791/is-the-4x5-chessboard-complex-a-link-complement}.

% General web links: \href [The On-Line Encyclopedia of Integer Sequences]{http://www.research.att.com/~njas/sequences/}

## Bibliography

% Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)

* D. Eppstein \href [MathOverFlow thread]{http://mathoverflow.net/questions/36791/is-the-4x5-chessboard-complex-a-link-complement}

* indicates original appearance(s) of problem.