An index formula for the intersection Euler characteristic of an infinite cone

详细信息    查看全文

• 作者：Ursula Ludwig ^{ursula.ludwig@uni-due.de}
• 刊名：Comptes Rendus Mathematique
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：355
• 期：1
• 页码：94-98
• 全文大小：239 K
• 卷排序：355

文摘

The aim of this note is to establish an index formula for the intersection Euler characteristic of a cone. The main actor of these notes is the model Witten Laplacian on the infinite cone. First, we study its spectral properties and establish a McKean–Singer-type formula. We also give an explicit formula for the zeta function of the model Witten Laplacian. In a second step, we apply local index techniques to the model Witten Laplacian. By combining these two steps, we express the absolute and relative intersection Euler characteristic of the cone as a sum of two terms, a term which is local, and a second term which is the Cheeger invariant.