Geometriae Dedicata

, Volume 80, Issue 1, pp 125–155

Witten Deformation and Polynomial Differential Forms

  • Michael Farber
  • Eugenii Shustin

DOI: 10.1023/A:1005267630882

Cite this article as:
Farber, M. & Shustin, E. Geometriae Dedicata (2000) 80: 125. doi:10.1023/A:1005267630882


As is well known, the Witten deformation dh of the De Rham complex computes the De Rham cohomology. In this paper, we study the Witten deformation on noncompact manifolds and restrict it on differential forms which behave polynomially near infinity. Such polynomial differential forms naturally appear on manifolds with the cylindrical structure. We prove that the cohomology of the Witten deformation dh acting on the complex of the polynomially growing forms (depends on h and) can be computed as the cohomology of the negative remote fiber ofh. We show that the assumptions of our main theorem are satisfied in a number of interesting special cases, including generic real polynomials on Rn.

polynomial differential forms De Rham complex real affine algebraic hypersurfaces 

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Michael Farber
    • 1
  • Eugenii Shustin
    • 2
  1. 1.School of Mathematical SciencesTel Aviv University, Ramat AvivTel AvivIsrael
  2. 2.School of Mathematical SciencesTel Aviv University, Ramat AvivTel AvivIsrael. E-mail

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