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1
Content available remote

The relative coincidence Nielsen number

100%
Jezierski J.
Fundamenta Mathematicae
|
1996
|
tom 149
|
nr 1
1-18
EN
We define a relative coincidence Nielsen number $N_{rel}(f,g)$ for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing $N_{rel}(f,g)$ by the ordinary Nielsen numbers.
2
Content available remote

On generalizing the Nielsen coincidence theory to non-oriented manifolds

100%
Jezierski J.
Banach Center Publications
|
1999
|
tom 49
|
nr 1
189-202
EN
We give an outline of the Nielsen coincidence theory emphasizing differences between the oriented and non-oriented cases.
3
Content available remote

Weak Wecken's theorem for periodic points in dimension 3

100%
Jezierski J.
Fundamenta Mathematicae
|
2003
|
tom 180
|
nr 3
223-239
EN
We prove that a self-map f: M → M of a compact PL-manifold of dimension ≥ 3 is homotopic to a map with no periodic points of period n iff the Nielsen numbers $N(f^{k})$ for k dividing n all vanish. This generalizes the result from [Je] to dimension 3.
4
Content available remote

The Nielsen coincidence theory on topological manifolds

100%
Jezierski J.
Fundamenta Mathematicae
|
1993
|
tom 143
|
nr 2
167-178
EN
We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.
5
Content available remote

The coincidence Nielsen number for maps into real projective spaces

100%
Jezierski J.
Fundamenta Mathematicae
|
1991-1992
|
tom 140
|
nr 2
121-136
EN
We give an algorithm to compute the coincidence Nielsen number N(f,g), introduced in [DJ], for pairs of maps into real projective spaces.
6
Content available remote

The semi-index product formula

100%
Jezierski J.
Fundamenta Mathematicae
|
1991-1992
|
tom 140
|
nr 2
99-120
EN
We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula    |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| $(f_b,g_b:p^{-1}(b) ∩ A)$ to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and $N(f_b,g_b)$.
7
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Lefschetz coincidence formula on non-orientable manifolds

64%
Gonçalves D. L., Jezierski J.
Fundamenta Mathematicae
|
1997
|
tom 153
|
nr 1
1-23
EN
We generalize the Lefschetz coincidence theorem to non-oriented manifolds. We use (co-) homology groups with local coefficients. This generalization requires the assumption that one of the considered maps is orientation true.
8
Content available remote

Minimal number of periodic points for smooth self-maps of S³

64%
Graff G., Jezierski J.
Fundamenta Mathematicae
|
2009
|
tom 204
|
nr 2
127-144
EN
Let f be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3 and r a fixed natural number. A topological invariant $D^m_r[f]$, introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of r-periodic points for all smooth maps homotopic to f. In this paper we calculate $D³_r[f]$ for all self-maps of S³.
9
Content available remote

The Nielsen product formula for coincidences

38%
Jezierski J.
Fundamenta Mathematicae
|
1990
|
tom 134
|
nr 3
183-212
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