论文标题
同源性辅导和双曲线三序列的几何形状
Homology cobordism and the geometry of hyperbolic three-manifolds
论文作者
论文摘要
研究三维同源性共同体群体的结构研究的主要挑战是了解双曲几何和同源性恢复性之间的相互作用。在本文中，对于双曲同源球体$ y $，我们在不可减至的解决方案之间的相对分级与seiberg-intent方程的相对分级和可简化的方程之间的相对分级界定，从光谱和$ y $的riemannian几何形状来看。使用此功能，我们可以在单极浮子同源性（及其$ \ Mathrm {pin}（2）$ - epivariant的细化中产生的一些数值不变式上提供明确的界限。我们将其应用于研究由双曲线同源性生成的同源性共生组的亚组，满足某些自然几何约束。
A major challenge in the study of the structure of the three-dimensional homology cobordism group is to understand the interaction between hyperbolic geometry and homology cobordism. In this paper, for a hyperbolic homology sphere $Y$ we derive explicit bounds on the relative grading between irreducible solutions to the Seiberg-Witten equations and the reducible one in terms of the spectral and Riemannian geometry of $Y$. Using this, we provide explicit bounds on some numerical invariants arising in monopole Floer homology (and its $\mathrm{Pin}(2)$-equivariant refinement). We apply this to study the subgroups of the homology cobordism group generated by hyperbolic homology spheres satisfying certain natural geometric constraints.
