piecewise linear manifold
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2017 ◽  
Vol 164 (2) ◽  
pp. 369-380
Author(s):  
CHRISTIAN LANGE

AbstractWe prove that every piecewise linear manifold of dimension up to four on which a finite group acts by piecewise linear homeomorphisms admits a compatible smooth structure with respect to which the group acts smoothly.


Author(s):  
C. Kearton

It is well known that a regular neighbourhood of a polyhedron in a piecewise linear manifold may be regarded as a simplicial mapping cylinder. The aim of this paper is to show that if the polyhedron is a locally unknotted submanifold of the interior then the class of maps giving rise to such regular neighbourhoods has a simple characterization. At the same time, it is possible to answer the question: Given a simplicial map f defined on a combinatorial manifold, when is the image of f also a combinatorial manifold? Marshall Cohen has answered this question when the image is required to be isomorphic to the domain; the methods used here are those developed in (1), to which the reader is referred for definitions and notation.


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