Abstract:
Elliptic complexes on a manifold with boundary whose differentials are Boutet de Monvel operators are studied. An Atiyah–Bott–Lefschetz type formula is obtained for such complexes.
Citation:
A. V. Brenner, M. A. Shubin, “The Atiyah–Bott–Lefschetz formula for elliptic complexes on a manifold with boundary”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 38, VINITI, Moscow, 1990, 119–183; J. Soviet Math., 64:4 (1993), 1069–1111
\Bibitem{BreShu90}
\by A.~V.~Brenner, M.~A.~Shubin
\paper The Atiyah--Bott--Lefschetz formula for elliptic complexes on a~manifold with boundary
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1990
\vol 38
\pages 119--183
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd127}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1156775}
\zmath{https://zbmath.org/?q=an:0738.58043|0784.58056}
\transl
\jour J. Soviet Math.
\yr 1993
\vol 64
\issue 4
\pages 1069--1111
\crossref{https://doi.org/10.1007/BF01097408}
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https://www.mathnet.ru/eng/intd127
https://www.mathnet.ru/eng/intd/v38/p119
This publication is cited in the following 5 articles:
N. R. Orlova, “Lefschetz formula for nonlocal elliptic problems associated with a bundle”, Math. Notes, 116:2 (2024), 390–393
N. R. Izvarina, A. Yu. Savin, “An Atiyah–Bott–Lefschetz Theorem for Relative Elliptic Complexes”, Lobachevskii J Math, 43:10 (2022), 2675
Rung-Tzung Huang, Yoonweon Lee, “Lefschetz fixed point formula on a compact Riemannian manifold with boundary for some boundary conditions”, Geom Dedicata, 181:1 (2016), 43
Francesco Bei, “The $L^2$ L 2 -Atiyah–Bott–Lefschetz theorem on manifolds with conical singularities: a heat kernel approach”, Ann Glob Anal Geom, 44:4 (2013), 565
A. M. Kytmanov, S. G. Myslivets, N. N. Tarkhanov, “On a holomorphic Lefschetz formula in strictly pseudoconvex subdomains of complex manifolds”, Sb. Math., 195:12 (2004), 1757–1779
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