Bounding volume by systoles of 3-manifolds

Mikhail G. Katz; Yuli B. Rudyak

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Bounding volume by systoles of 3-manifolds

机译：以3个歧管的收缩为界

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摘要

We prove a new systolic volume lowei bound for no n-or rentable n-manifolds, involving the stable 1-systole as well as the codimension-1 systole with coefficients in Z2. As an application, we prove that Lusternik-Schnirelmann category and systolic category agree for non-orientable closed manifolds of dimension 3, extending our earlier result in the orientable case,. Finally, we prove the homotopy invar iance of systolic category.

机译：我们证明了没有n或可租用n流形的新收缩期容积低限，涉及稳定的1收缩期以及系数为Z2的codimension-1收缩期。作为一个应用，我们证明Lusternik-Schnirelmann类和收缩类对于3维的不可定向的闭合歧管是一致的，从而扩展了我们在可定向情况下的早期结果。最后，我们证明了收缩类别的同伦不变性。

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《The Journal of the London Mathematical Society》 |2008年第2期|共11页
作者
Mikhail G. Katz; Yuli B. Rudyak;
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正文语种 eng
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专利

1. Bounding volume by systoles of 3-manifolds [J] . Mikhail G. Katz, Yuli B. Rudyak The Journal of the London Mathematical Society . 2008,第2期

机译：以3个歧管的收缩为界
2. Volume and topology of bounded and closed hyperbolic 3-manifolds [J] . JASON DEBLOIS, PETER B. SHALEN Communications in analysis and geometry . 2009,第5期

机译：有界和封闭双曲3-流形的体积和拓扑
3. The volume of a closed hyperbolic 3-manifold is bounded by #pi# times the length of any presentation of its fundamental group [J] . Daryl Cooper Proceedings of the American Mathematical Society . 1999,第3期

机译：封闭的双曲3流形的体积由＃pi＃乘以其基本组的任何表示长度的边界
4. A polynomial time algorithm to compute quantum invariants of 3-manifolds with bounded first Betti number [C] . Clement Maria, Jonathan Spreer Annual ACM-SIAM Symposium on Discrete Algorithms . 2017

机译：多项式时间算法计算3个歧管的量子不变性，其中有界第一Betti号
5. Implicit bounding volumes and bounding volume hierarchies [D] . Nguyen, An 2006

机译：隐式边界体积和边界体积层次结构
6. A comparison of right ventricular volume change during systole obtained using the monoplane Simpson’s method in two-dimensional echocardiographic apical four-chamber view with right ventricular volume change obtained using a prisma model reflecting the systolic long-axis shortening of the right ventricle of the heart: A pilot study [O] . K Loiske, K Emilsson 2008

机译：在二维超声心动图心尖四腔视图中使用单平面Simpson方法获得的收缩期右心室容积变化与使用反映心脏右心室的收缩期长轴缩短的棱镜模型获得的右心室容积变化的比较：初步研究
7. Bounding volume by systoles of 3-manifolds [O] . Mikhail G. Katz, Yuli, B. Rudyak 2012

机译：通过3个流形的收缩来限定体积
8. Towards Lower Bounds for Complexity of 3-Manifolds: A Program [R] . Anisov, S. 2001

机译：对于3流形复杂性的较低界限：一个程序

Bounding volume by systoles of 3-manifolds

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