An Atiyah–Bott–Lefschetz Theorem for Relative Elliptic Complexes

Relative elliptic theory is a theory of elliptic operators for pairs of closed smooth manifolds, where is a submanifold in . We consider geometric endomorphisms of complexes in this theory and prove an analogue of Atiyah–Bott–Lefschetz fixed-point formula for such endomorphisms.

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Published in:Lobachevskii journal of mathematics 2022-10, Vol.43 (10), p.2675-2684
Main Authors: Izvarina, N. R., Savin, A. Yu
Format: Article
Language:English
Subjects:
Algebra
Analysis
Fixed points (mathematics)
Geometry
Manifolds (mathematics)
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Probability Theory and Stochastic Processes
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container_title Lobachevskii journal of mathematics
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Savin, A. Yu
description Relative elliptic theory is a theory of elliptic operators for pairs of closed smooth manifolds, where is a submanifold in . We consider geometric endomorphisms of complexes in this theory and prove an analogue of Atiyah–Bott–Lefschetz fixed-point formula for such endomorphisms.
doi_str_mv 10.1134/S1995080222130170
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subjects Algebra
Analysis
Fixed points (mathematics)
Geometry
Manifolds (mathematics)
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Probability Theory and Stochastic Processes
title An Atiyah–Bott–Lefschetz Theorem for Relative Elliptic Complexes
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