Ike, Yuichi Microlocal Lefschetz classes of graph trace kernels. (English) Zbl 1343.32006 Publ. Res. Inst. Math. Sci. 52, No. 1, 83-101 (2016). Let \(X\) be a \(C^\infty\)-manifold and let \(\phi: X \rightarrow X\) be a morphism. The author defines a \(\phi\)-graph trace kernel slightly generalizing the corresponding construction on manifolds introduced by M. Kashiwara and P. Schapira [J. Inst. Math. Jussieu 13, No. 3, 487–516 (2014; Zbl 1327.14083)]. He then discusses some basic properties of the microlocal Lefschetz class in this setting. Indeed, his main result is the functoriality of microlocal Lefschetz classes with respect to the composition of graph trace kernels. As an application, the microlocal Lefschetz fixed point formula for constructible sheaves on a real analytic manifolds is obtained [Y. Matsui and K. Takeuchi, Int. Math. Res. Not. 2010, No. 5, 882–913 (2010; Zbl 1198.32003)]. Reviewer: Aleksandr G. Aleksandrov (Moskva) MSC: 32C38 Sheaves of differential operators and their modules, \(D\)-modules 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) Keywords:microlocal sheaf theory; trace kernels; Lefschetz classes; Lefschetz fixed point formulas; constructible sheaves; real analytic manifolds Citations:Zbl 1327.14083; Zbl 1198.32003 PDFBibTeX XMLCite \textit{Y. Ike}, Publ. Res. Inst. Math. Sci. 52, No. 1, 83--101 (2016; Zbl 1343.32006) Full Text: DOI arXiv References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.