Positive (p,n)-intermediate scalar curvature and cobordism
Positive (p,n)-intermediate scalar curvature and cobordism
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DOI：
10.1016/j.geomphys.2022.104625
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发表时间：
2021-10
影响因子：
1.5
通讯作者：
M. Burkemper;C. Searle;M. Walsh
中科院分区：
文献类型：
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作者：
M. Burkemper;C. Searle;M. Walsh
在本文中，我们考虑一个众所周知的建设由于Gromov和劳森，Schoen和丘，Gajer，和沃尔什，它允许扩展的度量的正标量曲率的余维至少为3的手术的痕迹，以度量的正标量曲率，这是一个产品附近的边界。我们将这个构造推广到（p，n）-中间标量曲率，0≤ p≤ n− 2，余维至少为p+ 3的手术。然后，我们用它来推广一个著名的定理的卡尔。设Rsp，n> 0（M）表示n-流形M上的正（p，n）-中间标量曲率度量空间，我们证明了对于0≤ p≤ 2 n− 3和n≥ 2，对于一个允许正（p，4 n − 1）-中间标量曲率度量的闭自旋（4 n − 1）-流形M，Rsp，4 n− 1> 0（M）有无穷多个路径分量。
In this paper we consider a well-known construction due to Gromov and Lawson, Schoen and Yau, Gajer, and Walsh which allows for the extension of a metric of positive scalar curvature over the trace of a surgery in codimension at least 3 to a metric of positive scalar curvature which is a product near the boundary. We extend this construction for (p, n)-intermediate scalar curvature for 0≤ p≤ n− 2 for surgeries in codimension at least p+ 3. We then use it to generalize a well known theorem of Carr. Letting R s p, n> 0 (M) denote the space of positive (p, n)-intermediate scalar curvature metrics on an n-manifold M, we show for 0≤ p≤ 2 n− 3 and n≥ 2, that for a closed, spin,(4 n− 1)-manifold M admitting a metric of positive (p, 4 n− 1)-intermediate scalar curvature, R s p, 4 n− 1> 0 (M) has infinitely many path components.