Koszul's Splitting Theorem and the Super Atiyah Class

Kowshik Bettadapura

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arXiv · 2009.00177

Koszul's Splitting Theorem and the Super Atiyah Class

Kowshik Bettadapura

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Abstract

In this article we present a self-contained account of two important results in complex supergeometry: (1) Koszul's Splitting theorem and (2) Donagi and Witten's decomposition of the super Atiyah class. These results are related in the same sense that global holomorphic connections on a holomorphic vector bundle are `related' to the Atiyah class of that vector bundle---the latter being the obstruction to the existence of the former. In complex supergeometry: Koszul's theorem pertains to the existence of supermanifold splittings whereas the super Atiyah class accordingly pertains to obstructions to the existence of splittings.

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BibTeX RIS

Kowshik Bettadapura. 2020-09-01. Koszul's Splitting Theorem and the Super Atiyah Class. https://arxiv.org/abs/2009.00177

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