This chapter contains the needed tools from foliation theory. It begins with basic concepts, like holonomy, foliated maps and foliated flows, Riemannian foliations, and some types of foliations of codimension one. Next, we recall the special features of differential forms, currents, and de Rham operators on foliated manifolds. Analysis of Witten’s perturbation on Riemannian foliations of bounded geometry is another needed ingredient.

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Foliation Tools

  • Jesús A. Álvarez López,
  • Yuri A. Kordyukov,
  • Eric Leichtnam

摘要

This chapter contains the needed tools from foliation theory. It begins with basic concepts, like holonomy, foliated maps and foliated flows, Riemannian foliations, and some types of foliations of codimension one. Next, we recall the special features of differential forms, currents, and de Rham operators on foliated manifolds. Analysis of Witten’s perturbation on Riemannian foliations of bounded geometry is another needed ingredient.