Open Problem Garden

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.

Keywords: knot theory, links, chessboard complex

Posted by rybu
updated September 4th, 2010

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Arthur

Hoffmann-Ostenhof

Graph Theory » Basic G.T. » Cycles

Strong 5-cycle double cover conjecture ★★★

Author(s): Arthur; Hoffmann-Ostenhof

Conjecture Let $C$ be a circuit in a bridgeless cubic graph $G$ . Then there is a five cycle double cover of $G$ such that $C$ is a subgraph of one of these five cycles.

Keywords: cycle cover

Posted by arthur
updated November 24th, 2011

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2-knot

knot theory

Gordon

Topology

Unsolvability of word problem for 2-knot complements ★★★

Author(s): Gordon

Problem Does there exist a smooth/PL embedding of $S^2$ in $S^4$ such that the fundamental group of the complement has an unsolvable word problem?