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Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms
Abstract
Let M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map f: M-->M. This task is related to determining a topological invariant D^4_r[f], defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of iterations. Previously, the invariant was computed for self-maps of some 3-manifolds. In this paper, we compute the invariants D^4_r[f] for the self-maps of closed 1-connected smooth 4-manifolds with definite intersection forms (i.e., connected sums of complex projective planes). We also present some efficient algorithmic approach to investigate that problem.
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Authors (4)
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Haibao Duan
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Jerzy Jezierski
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s11784-024-01108-9
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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Journal of Fixed Point Theory and Applications
no. 26,
ISSN: 1661-7738 - Language:
- English
- Publication year:
- 2024
- Bibliographic description:
- Duan H., Graff G., Jezierski J., Myszkowski A.: Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms// Journal of Fixed Point Theory and Applications -Vol. 26,iss. Art id 23 (2024), s.1-21
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s11784-024-01108-9
- Sources of funding:
- Verified by:
- Gdańsk University of Technology
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