TITLE

Examples of Rational Toral Rank Complex

AUTHOR(S)
Yamaguchi, Toshihiro
PUB. DATE
January 2012
SOURCE
International Journal of Mathematics & Mathematical Sciences;2012, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
There is a CW complex Τ(X), which gives a rational homotopical classification of almost free toral actions on spaces in the rational homotopy type of X associated with rational toral ranks and also presents certain relations in them. We call it the rational toral rank complex of X. It represents a variety of toral actions. In this note, we will give effective 2-dimensional examples of it when X is a finite product of odd spheres. This is a combinatorial approach in rational homotopy theory.
ACCESSION #
86746616

 

Related Articles

  • Quantitative Homotopy Theory in Topological Data Analysis. Blumberg, Andrew; Mandell, Michael // Foundations of Computational Mathematics;Dec2013, Vol. 13 Issue 6, p885 

    This paper lays the foundations of an approach to applying Gromov's ideas on quantitative topology to topological data analysis. We introduce the 'contiguity complex', a simplicial complex of maps between simplicial complexes defined in terms of the combinatorial notion of contiguity. We...

  • GENERALIZED DAVIS-JANUSZKIEWICZ SPACES MULTICOMPLEXES AND MONOMIAL RINGS. TREVISAN, ALVISE J. // Homology, Homotopy & Applications;2011, Vol. 13 Issue 1, p205 

    We show that every monomial ring can be realized topo-logically by a certain topological space. This space is called a generalized Davis-Januszkiewicz space and can be thought of as a colimit over a multicomplex, a combinatorial object generalizing a simplicial complex. Furthermore, we show that...

  • DICOVERING SPACES. Fajstrup, Lisbeth // Homology, Homotopy & Applications;2003, Vol. 5 Issue 2, p1 

    Considers the definition of the universal dicovering space II. Image of space II; Dipaths of space II; Dihomotopies of dipaths; Cardinality of discovering spaces.

  • α-Covering Dimension.  // International Journal of Pure & Applied Sciences & Technology;Mar2011, Vol. 3 Issue 1, p1 

    The article offers information on a type of covering dimension, indicating its properties and characterizations. It cites the use of alpha-open sets in topological spaces to present a type of covering dimension. Moreover, it indicates that every finite alpha-open cover of X has an alpha-open...

  • Homotopy Characterization of ANR Function Spaces. Smrekar, Jaka // Journal of Function Spaces & Applications;2013, p1 

    Let Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a topological space. Let YX denote the space of continuous maps from X to Y equipped with the compact open topology. We show that if X is a compactly generated Tychonoff space and Y is not discrete, then...

  • A comparative study of two fundamental invariants of exotic $${\mathbb R^{4}}$$'s. Bou Khuzam, Mazen // Journal of Geometry;2011, Vol. 102 Issue 1/2, p19 

    We present a comparative study of two fundamental invariants of exotic $${\mathbb R^{4}}$$'s. The first invariant e( R) is defined intrinsically using the smooth compact submanifolds of R while the other ?( R) depends of the possibility of embedding R in some spin manifolds. We prove that ? is...

  • The exact traveling wave solutions to two integrable KdV6 equations. Li, Jibin; Zhang, Yi // Chinese Annals of Mathematics;Mar2012, Vol. 33 Issue 2, p179 

    The exact explicit traveling solutions to the two completely integrable sixth-order nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work. It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two...

  • Maximal dimension of invariant subspaces to systems of nonlinear evolution equations. Shen, Shoufeng; Qu, Changzheng; Jin, Yongyang; Ji, Lina // Chinese Annals of Mathematics;Mar2012, Vol. 33 Issue 2, p161 

    In this paper, the dimension of invariant subspaces admitted by nonlinear systems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator $\mathbb{F} = (F^1 ,F^2 )$ with orders { k, k} ( k ≥ k) preserves the invariant subspace...

  • Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions. Shuxia Wang // Journal of Function Spaces & Applications;2013, p1 

    When the spatial dimensions n = 2, the initial data u0 ∊ H¹, and the Hamiltonian H(u0 ) ≤ 1, we prove that the scattering operator is well defined in the whole energy space H¹ (R²) for nonlinear Schrödinger equation with exponential nonlinearity (eλ|u|² - 1)u, where...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics