Higgs 丛的 Morse 理论与超Kähler Kirwan 满射性
辛几何
2009-10-23 v2 微分几何
摘要
本文使用 Morse 理论方法计算紧 Riemann 曲面上半稳定秩二零次 Higgs 丛空间上的等变 Betti 数，该方法承袭 Atiyah 与 Bott 对半稳定全纯丛的原始思路。这给出了超Kähler Kirwan 映射在非固定行列式情形下为满射的一个自然证明。
引用
@article{arxiv.math/0701560,
title = {Morse Theory and Hyperkahler Kirwan Surjectivity for Higgs Bundles},
author = {Georgios Daskalopoulos and Jonathan Weitsman and Richard Wentworth and Graeme Wilkin},
journal= {arXiv preprint arXiv:math/0701560},
year = {2009}
}
备注
33 pages. Corrected Betti number formulae, added a description of the \Gamma_2-invariant cohomology in the fixed determinant case (correcting an earlier error), explained the Morse-Bott isomorphism (Proposition 3.1) in detail