Thurston分裂与C-原理
Thurston's fragmentation and c-principles
摘要：
在本文中，我们推广了Thurston的原来的想法，所谓的Mather-Thurston定理的叶状丛证明这个定理的PL同胚，contactormorphisms的新变种。这些版本回答了Gelfand -Fuks和格林伯格对PL叶理和Rybicki对contactomorphisms提出的问题。有趣的一点是，与著名的Segal-McDuff的Mather-Thurston定理证明相比，原始的Thurston方法给出了一个紧支撑的c-原理定理，而不需要知道开球上的相关局部陈述。在附录中，我们表明，瑟斯顿的分裂意味着非阿贝尔庞加莱对偶定理及其推广使用斑点复合体。
英文摘要：
In this paper, we generalize the original idea of Thurston for the so called Mather-Thurston's theorem for foliated bundles to prove new variants of this theorem for PL homeomorphisms, contactormorphisms. These versions answer questions posed by Gelfand -Fuks and Greenberg on PL foliations and Rybicki on contactomorphisms. The interesting point about the original Thurston's technique compared to the better known Segal-McDuff's proof of the Mather-Thurston theorem is that it gives a compactly supported c-principle theorem without knowing the relevant local statement on open balls. In the appendix, we show that Thurston's fragmentation implies the non-abelian Poincare duality theorem and its generalization using blob complexes.
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