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##  simpcomp / blowups.gd
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##  Functions for bistellar moves  
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##  $Id: bistellar.gd 41 2010-04-07 16:32:50Z jonathan $
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## <#GAPDoc Label="blowups">
## <Section Label="sec:bltheory"> <Heading>Theory</Heading>
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## 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/> 
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## 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.
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## For a very short introduction to simplicial blowups see <Ref Chap="sec:Blowups"/>, for further information see <Cite Key="Spreer09CombPorpsOfK3"/>.
## </Section>
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## <Section>
## <Heading>Functions related to simplicial blowups</Heading>
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## <#Include Label="SCBlowup"/>
## <#Include Label="SCMappingCylinder"/>
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## </Section>
##<#/GAPDoc>
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