We construct an uncountable family of groups of type $FP$. In contrast to
every previous construction of non-finitely presented groups of type $FP$ we do
not use Morse theory on cubical complexes; instead we use Gromov's graphical
small cancellation theory.Comment: 3 figures. Second version: two paragraphs added emphasizing the
  difference between our construction and Morse theoretic one

Brown, Thomas

Leary, Ian J

English

arXiv

We construct an uncountable family of groups of type $FP$. In contrast to
every previous construction of non-finitely presented groups of type $FP$ we do
not use Morse theory on cubical complexes; instead we use Gromov's graphical
small cancellation theory.Comment: 5 figures. Third version: major expansion to clarify some points from
  the second version, correction of gap in one proof, change in some
  terminology. Two extra figures added. Second version: two paragraphs added
  emphasizing the difference between our construction and Morse theoretic one

Groups of type $FP$ via graphical small cancellation

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