论文标题
$ \ ell^p $ - 空格的bott bott odecity定理和无穷大的粗略诺维科夫猜想
A Bott periodicity theorem for $\ell^p$-spaces and the coarse Novikov conjecture at infinity
论文作者
论文摘要
我们为$ \ ell^p $ -space（$ 1 \ leq p <\ infty $）制定并证明了bott ofiencity定理。对于适当的度量空间$ x $带有有界几何形状，我们在Infinity中介绍了$ k $ - 人类学的版本，由$ k _*^{\ infty}（x）$表示，而无限的roe代数为$ c^*_ _ _ _ _ _ {\ infty}（x）$。然后，粗汇编映射从$ \ lim_ {d \ to \ infty} k _*^{\ infty}（p_d（x））$到$ k _*（c^*_ {\ infty}（x）（x））$，称为Infinity的粗整理图。我们表明，为了证明诺维科夫的粗糙猜想，足以证明无穷大时的粗组装图是注射。结果，我们表明，粗糙的Novikov的猜想可容纳任何有界几何形状的度量空间，该度量将纤维的粗嵌入到$ \ ell^p $ -Space中。其中包括一个残留有限双曲线组的所有盒子空间和一大群紧凑型空间的圆锥锥，并由双曲线组采取动作。
We formulate and prove a Bott periodicity theorem for an $\ell^p$-space ($1\leq p<\infty$). For a proper metric space $X$ with bounded geometry, we introduce a version of $K$-homology at infinity, denoted by $K_*^{\infty}(X)$, and the Roe algebra at infinity, denoted by $C^*_{\infty}(X)$. Then the coarse assembly map descents to a map from $\lim_{d\to\infty}K_*^{\infty}(P_d(X))$ to $K_*(C^*_{\infty}(X))$, called the coarse assembly map at infinity. We show that to prove the coarse Novikov conjecture, it suffices to prove the coarse assembly map at infinity is an injection. As a result, we show that the coarse Novikov conjecture holds for any metric space with bounded geometry which admits a fibred coarse embedding into an $\ell^p$-space. These include all box spaces of a residually finite hyperbolic group and a large class of warped cones of a compact space with an action by a hyperbolic group.
