论文标题
较高的属于谎言组的适当动作，第2部分：具有边界的歧管的情况
Higher genera for proper actions of Lie groups, Part 2: the case of manifolds with boundary
论文作者
论文摘要
令G为有限连接的谎言组，让K为最大的紧凑型亚组。令m为边界的共同处理G-proper歧管，并具有g-不变度度量，该度量是在边界附近的产品类型。在对G的其他假设下，例如，它满足了快速的衰变状况，并且G/K具有非阳性的截面曲率，我们定义了与G上的平滑组共生相关的较高的Atiyah-Patodi-singer C^* - 与l^2 l^2 dirac cocycles in g in g g l^2 2 _ d_ d_ d_ d _ d_ d _ f in f in l^2 dirac dirac d d d d _ \ \ flocal d _ \ \ flocal d _ \ \ \ flocal。然后，我们为这些c^* - 索引建立了更高的索引公式，并使用它以引入更高的属M，从而推广到具有边界的歧管，我们在第1部分中已经建立的结果。我们的结果特别适用于Gimimple Lie lie groupG。我们非常适合使用合适的相对循环组合组和相对K Theory组之间的配对。
Let G be a finitely connected Lie group and let K be a maximal compact subgroup. Let M be a cocompact G-proper manifold with boundary, endowed with a G-invariant metric which is of product type near the boundary. Under additional assumptions on G, for example that it satisfies the Rapid Decay condition and is such that G/K has nonpositive sectional curvature, we define higher Atiyah-Patodi-Singer C^*-indices associated to smooth group cocycles on G and to a generalized G-equivariant Dirac operator D on M with L^2-invertible boundary operator D_\partial. We then establish a higher index formula for these C^*-indices and use it in order to introduce higher genera for M, thus generalizing to manifolds with boundary the results that we have established in Part 1. Our results apply in particular to a semisimple Lie group G. We use crucially the pairing between suitable relative cyclic cohomology groups and relative K-theory groups.
