单尖点双曲3-流形的体积与同调
几何拓扑
2014-10-01 v3
摘要
设 M 为恰好具有一个尖点的完备、有限体积、可定向双曲流形。若假设 pi_1(M) 没有同构于亏格2曲面群的子群，且满足以下条件之一：(a) 对某个素数 p，H_1(M;Z_p) 的维数至少为 5；或 H_1(M;Z_2) 的维数至少为 4，且由杯积生成的像在 H^2(M;Z_2) 中张成的子空间维数至多为 1，则 vol M > 5.06。若假设 H_1(M;Z_2) 的维数至少为 7，且 M 的紧核不包含亏格2的闭不可压缩曲面，则 vol M > 5.06。
引用
@article{arxiv.0707.4300,
title = {Volume and homology of one-cusped hyperbolic 3-manifolds},
author = {Marc Culler and Peter B. Shalen},
journal= {arXiv preprint arXiv:0707.4300},
year = {2014}
}
备注
31 pages. This version agrees with the published version of the paper, except that an error in the published abstract has been corrected. In particular, the result which applies to manifolds with mod 2 homology of dimension at least 7 is stronger and has a shorter proof than the corresponding result in version 2