Forms and cohomology of supermanifolds under review

✍ Scribed by C. Victoria

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 750 KB
• Volume: 26
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(97)00043-0

✦ Synopsis

It is shown that the particular generalization of the de Rham complex to smooth Berezin-Leites-Kostant supermanifolds proposed in Voronov and Zorich (1986, 1988) and Voronov (199 1) is not self-consistent.

Some additional conditions are needed in order to make it work. It is proved that when these conditions are taken into account the cohomology of the resultant complex is isomorphic to the usual de Rham cohomology of the underlying manifold.