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	Chern-Simons theory, surface separability, and volumes of 3-manifolds
	Derbez, Pierre ; Liu, Yi ; Wang, Shicheng
	2015
关键词	GRAPH MANIFOLDS INVARIANTS BUNDLES CIRCLE SPACE TORI
英文摘要	We study the set vol( M, G) of volumes of all representations where M is a closed oriented 3- manifold and G is either Iso(+)H(3) or Iso(e)SL(2)(R) By various methods, including relations between the volume of representations and the ChernSimons invariants of flat connections, and recent results of surfaces in 3- manifolds, we prove that any 3- manifold M with positive Gromov simplicial volume has a finite cover M with and that any non- geometric 3-manifold M containing at least one Seifert piece has a finite cover M with vol(M, Isoe SL2(R)) = {0}. We also find 3-manifolds M with positive simplicial volume but vol(M, Iso+ H 3) = {0}, and non-trivial graph manifolds M with vol(M, Isoe SL2(R)) = {0}, proving that it is in general necessary to pass to some finite covering to guarantee that vol(M, G) = {0}. Besides we determine vol(M, G) when M supports the Seifert geometry.; NSF [DMS-1308836]; NSFC [11371034]; SCI(E); ARTICLE; pderbez@gmail.com; yliumath@caltech.edu; wangsc@math.pku.edu.cn; 4; 933-974; 8
语种	英语
出处	SCI
出版者	JOURNAL OF TOPOLOGY
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/439171]
专题	数学科学学院
推荐引用方式 GB/T 7714	Derbez, Pierre,Liu, Yi,Wang, Shicheng. Chern-Simons theory, surface separability, and volumes of 3-manifolds. 2015-01-01.

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