Let M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension m ≥ 4. Using this approach we calculate the invariant in case r is a product of different odd primes. We also obtain an estimate for D^m_r [f] from below and above for some other natural numbers r.
Authors
- prof. dr hab. Grzegorz Graff link open in new tab ,
- Jerzy Jezierski
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1007/s11784-012-0076-1
- Category
- Publikacja w czasopiśmie
- Type
- artykuł w czasopiśmie wyróżnionym w JCR
- Language
- angielski
- Publication year
- 2012
