The L2-Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities: a heat kernel approach

被引：0

作者：

Bei, Francesco ^{[1
]}

机构：

[1] Humboldt Univ, Inst Math, D-10099 Berlin, Germany

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2013年 / 44卷 / 04期

关键词：

Atiyah-Bott-Lefschetz theorem; Elliptic complexes; Differential cone operators; Heat kernel; Geometric endomorphisms; Manifolds with conical singularities; FIXED-POINT THEOREM; ELLIPTIC COMPLEXES; LEFSCHETZ; EXPANSION; RESOLVENT; FORMULA; RHAM;

D O I：

10.1007/s10455-013-9382-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using an approach based on the heat kernel, we prove an Atiyah-Bott-Lefschetz theorem for the -Lefschetz numbers associated with an elliptic complex of cone differential operators over a compact manifold with conical singularities. We then apply our results to the case of the de Rham complex.

引用

页码：565 / 605

页数：41

共 5 条

[1] The Atiyah–Bott–Lefschetz Theorem for Manifolds with Conical Singularities
Vladimir Nazaikinskii
Bert-Wolfgang Schulze
Boris Sternin
Victor Shatalov
Annals of Global Analysis and Geometry, 1999, 17 : 409 - 439
[2] The Atiyah-Bott-Lefschetz theorem for manifolds with conical singularities
Nazaikinskii, V
Schulze, BW
Sternin, B
Shatalov, V
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 1999, 17 (05) : 409 - 439
[3] ATIYAH-BOTT-LEFSCHETZ THEOREM FOR MANIFOLDS WITH BOUNDARY
BRENNER, AV
SHUBIN, MA
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1981, 15 (04) : 286 - 287
[4] An Atiyak-Bott-Lefschetz formula for elliptic operators on manifolds with conical singularities
Nazaikinskii, VE
Sternin, BY
Shatalov, VE
Schulze, BV
DOKLADY AKADEMII NAUK, 1999, 367 (03) : 303 - 306
[5] The L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document}-Atiyah–Bott–Lefschetz theorem on manifolds with conical singularities: a heat kernel approach
Francesco Bei
Annals of Global Analysis and Geometry, 2013, 44 (4) : 565 - 605

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