The Problems of Dimension Four, and Some Ramifications

Valentin Poénaru ()
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Valentin Poénaru: Laboratoire de mathematiques, Université Paris-Sud XI, CEDEX, 91405 Orsay, France

Mathematics, 2023, vol. 11, issue 18, 1-6

Abstract: In this short note, I present a very quick review of the peculiarities of dimension four in geometric topology. I consider, in particular, the role of geometric simple connectivity (which means handle decomposition without handles of index one) for both closed manifolds and open manifolds and for finitely presented groups, together with some of recent developments in geometric group theory.

Keywords: DIFF category; geometric simple connectivity; 4-dimensional topology; finitely presented groups; QSF property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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