Hodge 谱能否区分 orbifold 与流形?第一部分
微分几何
2021-08-17 v2
摘要
我们通过计算与 -谱相关的热不变量,考察紧致黎曼 orbifold 的奇异集与 -形式上的 Hodge Laplacian 谱之间的关系。我们证明:只要奇异集的余维数 ,对应的 Hodge Laplacian 的 -谱热不变量与 -谱热不变量一起足以区分带奇点的 orbifold 与流形。这对于维数 的情形已足以区分 orbifold 与流形。
引用
@article{arxiv.2106.07882,
title = {Do the Hodge spectra distinguish orbifolds from manifolds? Part 1},
author = {Katie Gittins and Carolyn Gordon and Magda Khalile and Ingrid Membrillo Solis and Mary Sandoval and Elizabeth Stanhope},
journal= {arXiv preprint arXiv:2106.07882},
year = {2021}
}
备注
Part 2, joint with Juan Pablo Rossetti, will appear. V1 contained in addition to the results in Part 1 sections that examined information contained in the individual $p$-spectra. After realizing that Rossetti had overlapping results, we split the original paper into the current Part 1 together with a strengthened Part 2, joint with Rossetti, that combines our work on the individual $p$-spectra