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.
Authors
- Haibao Duan,
- prof. dr hab. Grzegorz Graff link open in new tab ,
- Jerzy Jezierski,
- dr Adrian Myszkowski link open in new tab
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1007/s11784-024-01108-9
- Category
- Publikacja w czasopiśmie
- Type
- artykuły w czasopismach
- Language
- angielski
- Publication year
- 2024