WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY

Motivated by the Landau-Ginzburg model, we study Witten deformation on a noncompact manifold with bounded geometry, together some tameness condition growth of Morse function $f$ near infinity. We prove that cohomology $d_{Tf}$ acting complex smooth $L^2$ forms is isomorphic to Thom-Smale as well relative certain pair $(M, U)$ for sufficiently large $T$. establish an Agmon estimate eigenforms Laplacian which plays essential role in identifying these cohomologies via Witten's instanton complex, defined terms eigenspaces small eigenvalues. As application obtain strong inequalities this setting.