Culturations，immersions，mappability和Habegger的问题
Cubulations, immersions, mappability and a problem of Habegger
摘要：
本文的目的（启发从一个问题的Habegger）是描述一套三次分解的紧凑型流形模出一组组合移动类似的bistellar移动考虑Pachner，我们称之为泡沫移动。从这个集合到流形中余维为1的浸入的协边群上构造满射。流形和浸入的连通和诱导乘法结构，这是尊重这个满射。我们证明了对于足够大的$n$（称为可映射的），组合映射到${\bf R}^n$的标准分解中的那些分解是等价的.最后对2-球面的构造进行了分类。
英文摘要：
The aim of this paper (inspired from a problem of Habegger) is to describe the set of cubical decompositions of compact manifolds mod out by a set of combinatorial moves analogous to the bistellar moves considered by Pachner, which we call bubble moves. One constructs a surjection from this set onto the the bordism group of codimension one immersions in the manifold. The connected sums of manifolds and immersions induce multiplicative structures which are respected by this surjection. We prove that those cubulations which map combinatorially into the standard decomposition of ${\bf R}^n$ for large enough $n$ (called mappable), are equivalent. Finally we classify the cubulations of the 2-sphere.
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