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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Bibliographic Details
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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Description
Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080222130170