共查询到20条相似文献,搜索用时 0 毫秒
1.
P. Christopher Staecker 《Journal of Fixed Point Theory and Applications》2009,5(2):237-247
We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister
trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister
trace in coincidence theory. 相似文献
2.
Evelyn L. Hart 《Topology and its Applications》2006,153(9):1399-1420
Let denote a periodic self map of minimal period m on the orientable surface of genus g with g>1. We study the calculation of the Nielsen periodic numbers NPn(f) and NΦn(f). Unlike the general situation of arbitrary maps on such surfaces, strong geometric results of Jiang and Guo allow for straightforward calculations when n≠m. However, determining NPm(f) involves some surprises. Because fm=idFg, fm has one Nielsen class Em. This class is essential because L(idFg)=χ(Fg)=2−2g≠0. If there exists k<m with L(fk)≠0 then Em reduces to the essential fixed points of fk. There are maps g (we call them minLef maps) for which L(gk)=0 for all k<m. We show that the period of any minLef map must always divide 2g−2. We prove that for such maps Em reduces algebraically iff it reduces geometrically. This result eliminates one of the most difficult problems in calculating the Nielsen periodic point numbers and gives a complete trichotomy (non-minLef, reducible minLef, and irreducible minLef) for periodic maps on Fg.We prove that reducible minLef maps must have even period. For each of the three types of periodic maps we exhibit an example f and calculate both NPn(f) and NΦn(f) for all n. The example of an irreducible minLef map is on F4 and is of maximal period 6. The example of a non-minLef map is on F2 and has maximal period 12 on F2. It is defined geometrically by Wang, and we provide the induced homomorphism and analyze it. The example of an irreducible minLef map is a map of period 6 on F4 defined by Yang. No algebraic analysis is necessary to prove that this last example is an irreducible minLef map. We explore the algebra involved because it is intriguing in its own right. The examples of reducible minLef maps are simple inversions, which can be applied to any Fg. Using these examples we disprove the conjecture from the conclusion of our previous paper. 相似文献
3.
Yuhong Liu 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3376-3381
Given a continuous function f:Sm+n−2→Rm, and n points u1,u2,…,un∈Sm+n−2; does there exist a rotation r∈SO(m+n−1) such that f(ru1)=f(ru2)=?=f(run)? In this paper, we study the property of a continuous map from a sphere to a Euclidean space by using the theory of Smith periodic transformation and Brouwer degree of map theorem. The conjecture is proved under the case of n=2 and m being even. Furthermore, this conjecture is proved for the case when uj⋅uj+1=λ and the dimension of the sphere is not less than m+n−2. This paper generalizes the Borsuk-Ulam theorem and then presents its application. 相似文献
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Let be a continuous map and a constant map between closed orientable surfaces of genus h,g, respectively. By definition the pair (f,c) has the Wecken property if f can be deformed into a map such that every coincidence classes of (f',c) is essential and consists of exactly one point. The main result is that (f,c) has the Wecken property if and only if where . Certain quadratic equations in free groups closely related to the coincidence problem are solved. Received January 26, 1999; in final form December 10, 1999 / Published online March 12, 2001 相似文献
6.
Jonathan A. Hillman 《Topology and its Applications》2011,158(3):468-478
We compute the p-primary components of the linking pairings of orientable 3-manifolds admitting a fixed-point free S1-action. Any linking pairing on a finite abelian group of odd order is realized by such a manifold. We find necessary and sufficient conditions for a pairing on an abelian 2-group to be the 2-primary component of such a linking pairing, and give simple examples which are not realizable by any Seifert fibred 3-manifold. 相似文献
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Tetsu Nishimoto 《Topology and its Applications》2007,154(9):1956-1960
We determine the Lusternik-Schnirelmann category of real Stiefel manifolds Vn,k and quaternionic Stiefel manifolds Xn,k for n?2k which is equal to the cup-length of the mod 2 cohomology of Vn,k and the integer cohomology of Xn,k, respectively. 相似文献
9.
Gábor Kassay Cornel Pintea 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3537-3545
In this paper we first provide a geometric interpretation of the Minty-Browder monotonicity which allows us to extend this concept to the so called h-monotonicity, still formulated in an analytic way. A topological concept of monotonicity is also known in the literature: it requires the connectedness of all preimages of the operator involved. This fact is important since combined with the local injectivity, it ensures global injectivity. When a linear structure is present on the source space, one can ask for the preimages to even be convex. In an earlier paper, the authors have shown that Minty-Browder monotone operators defined on convex open sets do have convex preimages, obtaining as a by-product global injectivity theorems. In this paper we study the preimages of h-monotone operators, by showing that they are not divisible by closed connected hypersurfaces, and investigate them from the dimensional point of view. As a consequence we deduce that h-monotone local homeomorphisms are actually global homeomorphisms, as the proved properties of their preimages combined with local injectivity still produce global injectivity. 相似文献
10.
Annals of Global Analysis and Geometry - We investigate the maximal open domain $${\mathscr {E}}(M)$$ on which the orthogonal projection map p onto a subset $$M\subseteq {{\mathbb {R}}}^d$$ can be... 相似文献
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We give an example of two JSJ decompositions of a group that are not
related by conjugation, conjugation of edge-inclusions, and slide
moves. This answers the question of Rips and Sela stated in [RS].On the other hand we observe that any two JSJ decompositions of a group
are related by an elementary deformation, and that strongly slide-free
JSJ decompositions are genuinely unique. These results hold
for the decompositions of Rips and Sela, Dunwoody and Sageev, and
Fujiwara and Papasoglu, and also for accessible decompositions. 相似文献
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14.
Richard S. Palais 《Journal of Fixed Point Theory and Applications》2007,2(2):221-223
We give a simple proof of the Banach contraction lemma.
The author dedicates this work to two friends from long ago, Professors Albrecht Dold and Ed Fadell 相似文献
15.
Jerzy Jezierski 《Topology and its Applications》2011,158(9):1113-1120
Shub and Sullivan noticed that there is a large gap between the least number of periodic points, taken over the family of continuous maps homotopic to a given self-map f and the analogous number taken over the family of smooth maps homotopic to f. In this paper we show that in the case of self-maps of solvmanifolds the minimal numbers of n-periodic points, in both categories, are equal. 相似文献
16.
Seung Won Kim 《Journal of Pure and Applied Algebra》2007,208(2):467-479
In this paper we study the Nielsen number of a self-map f:M→M of a compact connected surface with boundary. Let G=π1(M) be the fundamental group of M which is a finitely generated free group. We introduce a new algebraic condition called “bounded solution length” on the induced endomorphism φ:G→G of f and show that many maps which have no remnant satisfy this condition. For a map f that has bounded solution length, we describe an algorithm for computing the Nielsen number N(f). 相似文献
17.
Lê Minh Hà 《Topology》2005,44(1):217-229
We study a homotopy invariant of phantom maps called the Gray index. In particular, it is conjectured that the Gray index of an essential phantom map between finite-type spaces is always finite. We obtain some partial results on this conjecture, using a tower-theoretic interpretation of the Gray index. 相似文献
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Let (G, H) be an irreducible semisimple symmetric pair,P
G a parabolic subgroup. Suppose that theL-orbit of the base point in the flag manifoldG/P is open and writeS(L,P)={gG:gL
LP} for the compression semigroup of this orbit. We show that ifP is minimal andS(L, P)=G, then (G, H) is Riemannian and we give a geometric characterization of those cases whereS(L, P) has non-empty interior different fromG. IfG/H is a symmetric space of regular type, then we show under certain additional assumptions thatS(L, Q) is an Ol'shanskiî semigroup.Supported by a DFG Heisenberg-grant. 相似文献
20.
W. M. Mikulski 《Monatshefte für Mathematik》1995,119(1-2):63-77
LetA be a Weil algebra withp variables. We prove that forn-manifolds (np+2) the set of all natural operatorsT
*T
*
T
A
is a free finitely generated module over a ring canonically dependent onA. We construct explicitly the basis of this module. 相似文献