On the regularity of cylindrical algebraic decompositions

  • Acyr Locatelli

Student thesis: Doctoral ThesisPhD


Cylindrical algebraic decomposition is a powerful algorithmic technique in semi-algebraicgeometry. Nevertheless, there is a disparity between what algorithms output and whatthe abstract definition of a cylindrical algebraic decomposition allows. Some work hasbeen done in trying to understand what the ideal class of cylindrical algebraic decom-positions should be — especially from a topological point of view.We prove a special case of a conjecture proposed by Lazard in [22]; the conjecturerelates a special class of cylindrical algebraic decompositions to regular cell complexes.Moreover, we study the properties that define this special class of cell decompositions,as well as their implications for the actual topology of the cells that make up the celldecompositions.
Date of Award15 Apr 2016
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorGregory Sankaran (Supervisor) & James Davenport (Supervisor)


  • Cylindrical Algebraic Decomposition
  • regularity

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