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31.
R. Craggs 《Topology and its Applications》1988,30(3):237-252
The possibility is considered that the Andrews-Curtis conjecture, if false, may provide obstructions to the cancellation of 1- and 3-handles in a simply connected 4-manifold. An algebra is developed for the simultaneous algebraic reading of attaching maps for 2-handles and their duals, and it is shown that obstructions to 1- and 3-handle cancellation cannot bedetected in this algebra. 相似文献
32.
We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we confine ourselves to several topics on fixed points of self-maps on manifolds and polyhedra. Special attention is paid to connections with geometric group theory and dynamics, as well as some formal approaches. 相似文献
33.
A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints 下载免费PDF全文
<正>A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints is investigated.Nielsen equations and differential equations of motion for the holonomic mechanical system with unilateral constraints are established.The definition and the criterion of Mei symmetry for Nielsen equations in the holonomic systems with unilateral constraints under the infinitesimal transformations of Lie group are also given.The expressions of the structural equation and a type of new conserved quantity of Mei symmetry for Nielsen equations in the holonomic system with unilateral constraints are obtained.An example is given to illustrate the application of the results. 相似文献
34.
拓扑熵的一个下界估计 总被引:3,自引:0,他引:3
设X为局部闭路可缩的紧致空间,f为X的自映射,h(f)为f的拓扑熵,R∞(f)为f的渐近Reidemeister数,则有h(f)≥logR∞(f). 相似文献
35.
In this paper we study, the Reidemeister zeta function. We prove rationality and functional equations of the Reidemeister zeta function of an endomorphism of finite group. We also obtain these results for eventually commutative endomorphisms. These results are applied to the theory of Reidemeister and Nielsen numbers of self-maps of topological spaces. Our method is to identify the Reidemeister number of a group endomorphism with the number of fixed points in the unitary dual. As a consequence, we show that the Reidemeister torsion of the mapping torus of the unitary dual is a special value of the Reidemeister zeta function. We also prove certain congruences for Reidemeister numbers which are equivalent to a Euler product formula for the Reidemeister zeta function. The congruences are the same as those found by Dold for Lefschetz numbers. 相似文献
36.
Jerzy Jezierski Wacław Marzantowicz 《Bulletin of the Brazilian Mathematical Society》2005,36(2):205-224
A well-known example, given by Shub, shows that for any |d| ≥ 2 there is a self-map of the sphere Sn, n ≥ 2, of degree d for which the set of non-wandering points consists of two points. It is natural to ask which additional
assumptions guarantee an infinite number of periodic points of such a map. In this paper we show that if a continuous map
f : Sn → Sn commutes with a free homeomorphism g : Sn → Sn of a finite order, then f has infinitely many minimal periods, and consequently infinitely many periodic points. In other words the assumption of the
symmetry of f originates a kind of chaos. We also give an estimate of the number of periodic points.
*Research supported by KBN grant nr 2 P03A 045 22. 相似文献
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The definition and criterion of the form invariance of Nielsen equations are given. The relation between the form invariance and the Noether symmetry is studied. Some examples are given to illustrate the application of the result. 相似文献