The equivariant parametrized h-cobordism theorem, the non-manifold part
The equivariant parametrized h-cobordism theorem, the non-manifold part
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等变参数化 h 配边定理，非流形部分
DOI：
10.1016/j.aim.2022.108242
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发表时间：
2022
影响因子：
1.7
通讯作者：
Merling, Mona
中科院分区：
文献类型：
--
作者：
Malkiewich, Cary;Merling, Mona
构造了一个从光滑紧致G流形的悬挂G-谱<$G ∞ M到等变A-理论谱AG（M）的映射，并证明了它的纤维在不动点上是稳定h-协边谱的楔形.该映射被构造为谱Mackey函子的映射，它与不动点上的Tom Dieck型分裂公式相容。为了调和不同的定义的悬浮G-频谱作为一个频谱麦基函子，我们提出了一个新的视角频谱麦基函子，查看他们作为多函子索引类别的“环上的许多对象”和模块等。这种观点应该是独立的利益。
We construct a map from the suspension G-spectrum Σ G∞ 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 reconcile 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.