THE LEFSCHETZ NUMBER OF SEQUENCES OF TRACE CLASS CURVATURE

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TARKHANOV NIKOLAI; WALLENTA DANIEL

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Journal Paper

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Journal: MATHEMATICAL SCIENCES Year:2012 | Volume:6 | Issue:- Page(s): 1-8

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Title

THE LEFSCHETZ NUMBER OF SEQUENCES OF TRACE CLASS CURVATURE

Author(s)

TARKHANOV NIKOLAI | WALLENTA DANIEL | Issue Writer Certificate

Keywords

PERTURBED COMPLEXES

CURVATURE

LEFSCHETZ NUMBER

Abstract

For a sequence of Hilbert spaces and continuous linear operators, the CURVATURE is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra.Purpose: We wish to study those sequences for which the CURVATURE is ‘small’ at each step, e.g., belongs to a fixed operator ideal.Methods: Our methods are based on combining homological algebra with the theory of Fredholm operators in Hilbert spaces.Results: We elaborate the theory of Fredholm sequences and show that any Fredholm sequence of trace class CURVATURE can be reduced to a Fredholm complex. This allows one to introduce the LEFSCHETZ NUMBER for cochain self-mappings of Fredholm sequences of ‘small’ CURVATURE.Conclusion: Our results raise fixed point theory for Fredholm complexes of trace class CURVATURE.

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APA: Copy

TARKHANOV, NIKOLAI, & WALLENTA, DANIEL. (2012). THE LEFSCHETZ NUMBER OF SEQUENCES OF TRACE CLASS CURVATURE. MATHEMATICAL SCIENCES, 6(-), 1-8. SID. https://sid.ir/paper/322612/en

Vancouver: Copy

TARKHANOV NIKOLAI, WALLENTA DANIEL. THE LEFSCHETZ NUMBER OF SEQUENCES OF TRACE CLASS CURVATURE. MATHEMATICAL SCIENCES[Internet]. 2012;6(-):1-8. Available from: https://sid.ir/paper/322612/en

IEEE: Copy

NIKOLAI TARKHANOV, and DANIEL WALLENTA, “THE LEFSCHETZ NUMBER OF SEQUENCES OF TRACE CLASS CURVATURE,” MATHEMATICAL SCIENCES, vol. 6, no. -, pp. 1–8, 2012, [Online]. Available: https://sid.ir/paper/322612/en

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