论文标题
具有有界几何形状的非瘫痪歧管的Witten变形
Witten deformation for noncompact manifolds with bounded geometry
论文作者
论文摘要
在Landau-Ginzburg模型的启发下，我们研究了具有有界几何形状的非伴随歧管上的Witten变形，以及在Infinity附近的Morse功能$ f $的增长方面的某些驯服条件。我们证明，作用于光滑$ l^2 $形式的综合体的witten变形的共同体学对于$ f $的汤姆 - 梅勒综合体的同一个同构和一对$（m，u）$的相对共同学对于足够的大$ $ t $是同构。我们建立了Witten Laplacian特征形式的Agmon估计值，该估计在通过Witten的Instanton Complex识别这些共同体方面起着至关重要的作用，该复合物是根据Witten Laplacian的特征性特征的小特征值定义的。作为应用程序，我们在这种情况下获得了强烈的摩尔斯摩尔斯不平等现象。
Motivated by the Landau-Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function $f$ near infinity. We prove that the cohomology of the Witten deformation $d_{Tf}$ acting on the complex of smooth $L^2$ forms is isomorphic to the cohomology of Thom-Smale complex of $f$ as well as the relative cohomology of a certain pair $(M, U)$ for sufficiently large $T$. We establish an Agmon estimate for eigenforms of the Witten Laplacian which plays an essential role in identifying these cohomologies via Witten's instanton complex, defined in terms of eigenspaces of the Witten Laplacian for small eigenvalues. As an application we obtain the strong Morse inequalities in this setting.
