DIGITAL BOOKSHOP OF THE USC
Teoría de cobordismo e invariantes derivados asintóticos da traza da calor
- Autor/a
- Irimia Rega, Pablo
We examine the derived heat trace aymptotics in both the real and the complex settings for a generalized Witten perturbation on a Riemannian or Kählerian manifold.Firstly, we examine the local index density of the perturbed De Rham complex and of the perturbed Dolbeault complex. In the former case, the generalized Witten perturbation is realiced in the Riemann manifold, using a closed 1-form Θ. We show that the perturbed index density is independent of Θ. In the latter, we asume the underlying geometry to be Kähler. Now, we introduce the generalized Witten perturbation, using a (1, 0)-form Θ with ∂Θ = 0. We give an explicit description of the associated index density which shows that it exhibits a nontrivial dependence on Θ. After that, we introduce the derived heat trace asymptotics. If the dimension is even, in the real context we show the integral of the local density for the derived heat trace asymptotics is proportional to the Euler class of the underlying manifold. In the complex setting, we, again, asume the manifold to be Kähler and show the integral of the local density for the derived heat trace asymptotics defined by the Dolbeault complex is a characteristic number of the complex tangent bundle and the twisting vector bundle. We compute this characteristic number if the complex dimension is 1 and 2.Finally, Cobordism theory is introduced in order to use it to compute the characteristic number in higher dimension. We start by analyzing cobordism theory in a general way. focus on the complex cobordism, since we want to use it in a future work, as a tool for our purpouses.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Publication Year
- 2024
- Serie
- 154b Publicaciones del Departamento de Geometría y Topología
- Availability
- Si
We examine the derived heat trace aymptotics in both the real and the complex settings for a generalized Witten perturbation on a Riemannian or Kählerian manifold.Firstly, we examine the local index density of the perturbed De Rham complex and of the perturbed Dolbeault complex. In the former case, the generalized Witten perturbation is realiced in the Riemann manifold, using a closed 1-form Θ. We show that the perturbed index density is independent of Θ. In the latter, we asume the underlying geometry to be Kähler. Now, we introduce the generalized Witten perturbation, using a (1, 0)-form Θ with ∂Θ = 0. We give an explicit description of the associated index density which shows that it exhibits a nontrivial dependence on Θ. After