共查询到20条相似文献,搜索用时 15 毫秒
1.
Let f, g : M N be two maps between two compact nilmanifolds with dim M dim N = n. In this paper, we show that either the Nielsen coincidence number N(f, g) = 0 or N(f, g) = R(f, g) where R(f, g) denotes the Reidemeister number of f and g. Furthermore, we show that if N(f, g) > 0 then the primary obstruction on(f, g) to deforming f and g to be coincidence free on the n-th skeleton of M is non-trivial.Received: 30 April 2004; revised: 20 July 2004 相似文献
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3.
Christoph Hamburger 《Mathematische Annalen》2006,334(4):775-782
We prove an analog of the Brouwer fixed point theorem for a map whose differential and adjoint are integrable with exponents n−1 and n/(n−1) respectively. Here Ω is a convex bounded open subset of Rn.
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4.
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
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S.L. Singh S.N. Mishra 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(6):2243-2248
Coincidence and fixed point theorems for single-valued and multi-valued maps generalizing recent results of Suzuki and Kikkawa are obtained. Various applications, including the existence of common solutions of certain functional equations are presented. 相似文献
6.
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
7.
The simplest condition characterizing quasi-finite CW complexes K is the implication XτhK⇒β(X)τK for all paracompact spaces X. Here are the main results of the paper:
Theorem 0.1.
If{Ks}s∈Sis a family of pointed quasi-finite complexes, then their wedge?s∈SKsis quasi-finite. 相似文献
8.
In this paper, when G is the circle S1 and M is a G-space, we study the rational homotopy type of the fixed point set MG, the homotopy fixed point set MhG, and the natural injection MG→MhG. 相似文献
9.
Suppose that M and N are orientable, closed, connected manifolds with free actions of compact Lie groups G and H of the same dimension, and suppose that u : G → H is a homomorphism. We study the degree of maps f : M → N that are “equivariant up to u”. For abelian actions and for a power map such maps satisfy the condition f(λx) = λ
r
x.
To Albrecht Dold and Edward Fadell 相似文献
10.
Leonard R. Rubin 《Topology and its Applications》2007,155(2):82-91
Suppose that K is a CW-complex. When we say that a space Y is an absolute co-extensor for K, we mean that K is an absolute extensor for Y, i.e., that for every closed subset A of Y and any map , there exists a map that extends f.Our main theorem will provide several statements that are equivalent to the condition that whenever K is a CW-complex and X is a space which is the topological sum of a countable collection of compact metrizable spaces each of which is an absolute co-extensor for K, then the Stone-?ech compactification of X is an absolute co-extensor for K. 相似文献
11.
Sierpiski proved that every countable set of mappings on an infinite set
X is
contained in a 2-generated subsemigroup of the semigroup of all mappings on
X. In this
paper we prove that every countable set of endomorphisms of an algebra
which has an infinite basis (independent generating set) is contained in a 2-generated subsemigroup
of the semigroup of all endomorphisms of
. 相似文献
12.
The group theoretic method is applied for solving problem of a unsteady free-convective laminar boundary-layer flow on a non-isothermal vertical plate under the effect of an external velocity and a magnetic field normal to the plate. The application of two-parameter transformation group reduces the number of independent variables, by two, and consequently the system of governing partial differential equations with the boundary and initial conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. The Runge–Kutta shooting method used to find the numerical solution of the velocity field, shear stress, heat transfer and heat flux has been obtained. The effect of the magnetic field on the velocity field and the Prandtl number on the heat transfer and heat flux has been discussed. 相似文献
13.
Smaïl Djebali Karima Hammache 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3440-3449
In this work, we present some new versions of fixed point theorems for nonexpansive maps and 1-set contractions defined on closed, convex, not necessarily bounded subsets of Banach spaces. Our proofs rely on a compactness result for an approximate fixed point set. The Kuratowski measure of noncompactness is used throughout. To illustrate the results obtained, some applications to Banach algebras and Hammerstein integral equations are provided. 相似文献
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James P. Lin 《Topology and its Applications》2009,156(10):1786-1800
Let p be an odd prime. Let be the fibre space induced from an H-map where K is a generalized Eilenberg MacLane space and X is a simply connected H-space. Such spaces occur frequently in Postnikov towers and connective covers. In this paper, we compute the mod p cohomology of as a ring. The ring depends on the structure of imf* and the structure of subkerf* as modules over the Steenrod algebra. 相似文献
16.
Let σ be an endomorphism of the free group on two generators and Φσ the trace map associated with σ. A polynomial P is said to be periodic for σ if, for some positive integer n, it is invariant under , i.e., . In this note we study the structure of the ring of periodic polynomials for σ. 相似文献
17.
Aaron Reite 《Journal of Pure and Applied Algebra》2008,212(6):1367-1380
In this paper we define model solvmanifold pairs and their diagonal type selfmaps in the tradition of Heath and Keppelmann. We derive an explicit formula for computing the relative Nielsen number N(F;X,A) on these spaces and selfmaps F:(X,A)→(X,A). We find that model solvmanifold pairs often exhibit interesting Schirmer theory, meaning N(F;X,A)>max{N(F),N(F|A)}. 相似文献
18.
Nielsen fixed point theory deals with the fixed point sets of self maps on compact polyhedra. In this note, we shall extend
it to stratified maps, to consider fixed points on (noncompact) strata. The extension was motivated by our recent work on
the braid forcing problem in which the deleted symmetric products are indispensable. The stratified viewpoint is theoretically
as natural as the equivariant Nielsen fixed point theory, while it can be more tractable computationally and more flexible
in applications.
This work was partially supported by an NSFC grant and a BMEC grant. 相似文献
19.
Peter Wong 《manuscripta mathematica》1999,98(2):243-254
Let f,g:X→M be maps between two closed connected orientable n-manifolds where M=G/K is the homogeneous space of left cosets of a compact connected Lie group G by a finite subgroup K. In this note, we obtain a simple formula for the Lefschetz coincidence number L(f,g) in terms of topological degree, generalizing some previously known formulas for fixed points. Our approach, by means of
Nielsen root theory, also allows us to give a simpler and more geometric proof of the fact that all coincidence classes of
f and g have coincidence index of the same sign.
Received: 3 March 1998 / Revised version: 29 June 1998 相似文献
20.
Younggi Choi 《Topology and its Applications》2008,155(12):1340-1349
We study the homology of gauge groups associated with principal SU(n) bundles over the four-sphere. After computing the mod p homology of based gauge groups of SU(n) by combined use of the Serre spectral sequence and the Eilenberg-Moore spectral sequence, we compute the modp homology of gauge groups of SU(n) using the Serre spectral sequence for the evaluation fibration. 相似文献