论文标题
均值参数化的$ h $ - 库伯斯定理，非manifold零件
The equivariant parametrized $h$-cobordism theorem, the non-manifold part
论文作者
论文摘要
我们从悬架$ g $ -spectrum $σ_g^\ infty m $中构建一张地图，即光滑的紧凑型$ g $ -manifold到eproivariant $ a $ a $ a $ a $ a spectrum $ a_g（m）$，我们显示其光纤在固定点上是稳定的$ h $ -cobordism spectra。该地图被构造为光谱Mackey函子的地图，它与固定点上的Tom Dieck样式分裂公式兼容。为了综合悬挂$ g $ -spectrum作为光谱Mackey函数的不同定义，我们对Spectral Mackey Foundors呈现了一个新的视角，将它们视为“许多对象上的戒指”的索引类别的多函数，以及此类模块。这种观点应该具有独立的利益。
We construct a map from the suspension $G$-spectrum $Σ_G^\infty M$ of a smooth compact $G$-manifold to the equivariant $A$-theory spectrum $A_G(M)$, and we show that its fiber is, on fixed points, a wedge of stable $h$-cobordism spectra. This map is constructed as a map of spectral Mackey functors, which is compatible with tom Dieck style splitting formulas on fixed points. In order to synthesize different definitions of the suspension $G$-spectrum as a spectral Mackey functor, we present a new perspective on spectral Mackey functors, viewing them as multifunctors on indexing categories for "rings on many objects" and modules over such. This perspective should be of independent interest.
