Results 31 to 40 of about 270 (43)
Twisted conjugacy classes in R. Thompson's group F [PDF]
arXiv, 2007 In this short article, we prove that any automorphism of the R. Thompson's group $F$ has infinitely many twisted conjugacy classes. The result follows from the work of Matthew Brin, together with a standard facts on R. Thompson's group $F$, and elementary properties of the Reidemeister numbers.
arxiv
A formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles [PDF]
Topological Methods in Nonlinear Analysis 33, 2009, p. 41-50, 2007 We give a formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles in terms of the Fox calculus. Our formula reduces the problem of computing the coincidence Reidemeister trace to the problem of distinguishing doubly twisted conjugacy classes in free groups.
arxiv
Point fixe lié à une orbite périodique d'un difféomorphisme de R2 [PDF]
Comptes Rendus de l'Academie des Sciences. Serie 1, Mathematique
310, 12 (1990) 831-833, 2007 Given a diffeomorphism of the plane, which has a periodic orbit, we show how Nielsen fixed point theory can be used to establish the existence of a fixed point which is linked with this periodic orbit.
arxiv
Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan [PDF]
Ergodic Theory and Dynamical Systems 12, 4 (1992) 677-682, 2007 Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic orbit.
arxiv
New directions in Nielsen-Reidemeister theory [PDF]
arXiv, 2007 The purpose of this expository paper is to present new directions in the classical Nielsen-Reidemeister fixed point theory. We describe twisted Burnside-Frobenius theorem, groups with $R_\infty$ \emph{property} and a connection between Nielsen fixed point theory and symplectic Floer homology.
arxiv
Twisted conjugacy classes for polyfree groups [PDF]
arXiv, 2008 Let $G$ be a finitely generated polyfree group. If $G$ has nonzero Euler characteristic then we show that $Aut(G)$ has a finite index subgroup in which every automorphism has infinite Reidemeister number. For certain $G$ of length 2, we show that the number of Reidemeister classes of every automorphism is infinite.
arxiv
Self-mapping Degrees of 3-Manifolds [PDF]
Osaka J. Math. 49 (2012), no. 1, 247--269, 2008 For each closed oriented 3-manifold $M$ in Thurston's picture, the set of degrees of self-maps on $M$ is given.
arxiv
Inscribing a regular crosspolytope [PDF]
arXiv, 2009 In this paper we prove that it is possible to inscribe a regular crosspolytope (multidimensional octahedron) into a smooth convex body in $\mathbb R^d$, where $d$ is an odd prime power. Some generalizations of this statement are also proved.
arxiv
A Poincaré-Hopf theorem for n-valued vector fields [PDF]
arXivThe Poincar\'e-Hopf theorem for line fields, as described in a paper of Crowley and Grant, is interpreted as a special case of a Poincar\'e-Hopf theorem for $n$-valued sections of a vector bundle over a closed manifold of the same dimension.
arxiv