## <#GAPDoc Label="blowups"> ## <Section Label="sec:bltheory"> <Heading>Theory</Heading> ## ## In this chapter functions are provided to perform simplicial blowups as ## well as the resolution of isolated singularities of certain types of ## combinatorial <M>4</M>-manifolds. As of today singularities where the ## link is homeomorphic to <M>\mathbb{R}P^3</M>, <M>S^2 \times S^1</M>, ## <M>S^2 \dtimes S^1</M> and the lens spaces <M>L(k,1)</M> are supported. ## In addition, the program provides the possibility to hand over additional ## types of mapping cylinders to cover other types of singularities.<P/> ## ## Please note that the program is based on a heuristic algorithm using ## bistellar moves. Hence, the search for a suitable sequence of bistellar ## moves to perform the blowup does not always terminate. However, ## especially in the case of ordinary double points (singularities of type ## <M>\mathbb{R}P^3</M>), a lot of blowups have already been successful. ## ## For a very short introduction to simplicial blowups see ## <Ref Chap="sec:Blowups"/>, for further information see ## <Cite Key="Spreer09CombPorpsOfK3"/>. ## </Section> ## ## <Section> ## <Heading>Functions related to simplicial blowups</Heading> ## ## <#Include Label="SCBlowup"/> ## <#Include Label="SCMappingCylinder"/> ## ## </Section> ##<#/GAPDoc>
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