scholarly journals Quasicomplexes and Lefschetz numbers

2013 ◽  
Vol 79 (3-4) ◽  
pp. 611-621
Author(s):  
Jörg Eschmeier
Keyword(s):  
Lefschetz Numbers

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Grzegorz Graff ◽  
Agnieszka Kaczkowska
Keyword(s):  
Natural Number ◽  
Homotopy Class ◽  
Periodic Points ◽  
Topological Invariant ◽  
Periodic Sequence ◽  
Connected Manifold ◽  
Lefschetz Numbers ◽  
Simply Connected Manifolds ◽  
Simply Connected

AbstractLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f.In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ℚ) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.

scholarly journals On Some Integral Invariants, Lefschetz Numbers and Induction Maps

1988 ◽  
Vol 11 (2) ◽  
pp. 289-302
Author(s):  
Akito FUTAKI ◽  
Kenji TSUBOI
Keyword(s):  
Integral Invariants ◽  
Lefschetz Numbers
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