scholarly journals ON THE TOPOLOGY OF T-DUALITY

2005 ◽  
Vol 17 (01) ◽  
pp. 77-112 ◽  
Author(s):  
ULRICH BUNKE ◽  
THOMAS SCHICK
Keyword(s):  
Homotopy Type ◽  
Cohomology Class ◽  
Dimensional Torus ◽  
Duality Transformation ◽  
Classifying Space ◽  
Simple Derivation ◽  
Torus Bundles ◽  
Twisted Cohomology ◽  
Higher Dimensional ◽  
Topological Version

We study a topological version of the T-duality relation between pairs consisting of a principal U(1)-bundle equipped with a degree-three integral cohomology class. We describe the homotopy type of a classifying space for such pairs and show that it admits a selfmap which implements a T-duality transformation. We give a simple derivation of a T-duality isomorphism for certain twisted cohomology theories. We conclude with some explicit computations of twisted K-theory groups and discuss an example of iterated T-duality for higher-dimensional torus bundles.

scholarly journals Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles

2017 ◽  
Vol 2019 (13) ◽  
pp. 4004-4046
Author(s):  
Corey Bregman
Keyword(s):  
Unit Circle ◽  
Dimensional Torus ◽  
Torus Bundle ◽  
Generating Set ◽  
Growth Series ◽  
Torus Bundles ◽  
Almost Convex ◽  
Higher Dimensional ◽  
Finite Index Subgroup ◽  
Almost Convexity

AbstractGiven a matrix $A\in SL(N,\mathbb{Z})$, form the semidirect product $G=\mathbb{Z}^N\rtimes_A \mathbb{Z}$ where the $\mathbb{Z}$-factor acts on $\mathbb{Z}^N$ by $A$. Such a $G$ arises naturally as the fundamental group of an $N$-dimensional torus bundle which fibers over the circle. In this article, we prove that if $A$ has distinct eigenvalues not lying on the unit circle, then there exists a finite index subgroup $H\leq G$ possessing rational growth series for some generating set. In contrast, we show that if $A$ has at least one eigenvalue not lying on the unit circle, then $G$ is not almost convex for any generating set.

scholarly journals Spherical posets from commuting elements

2018 ◽  
Vol 21 (4) ◽  
pp. 593-628 ◽  
Author(s):  
Cihan Okay
Keyword(s):  
Homotopy Type ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Universal Cover ◽  
Homotopy Equivalent ◽  
Classifying Space ◽  
Partially Ordered ◽  
Abelian Subgroups

AbstractIn this paper, we study the homotopy type of the partially ordered set of left cosets of abelian subgroups in an extraspecial p-group. We prove that the universal cover of its nerve is homotopy equivalent to a wedge of r-spheres where {2r\geq 4} is the rank of its Frattini quotient. This determines the homotopy type of the universal cover of the classifying space of transitionally commutative bundles as introduced in [2].

scholarly journals MAGNETIC MONOPOLES, BOGOMOL’NYI BOUND AND SL(2, ℤ) INVARIANCE IN STRING THEORY

1993 ◽  
Vol 08 (21) ◽  
pp. 2023-2036 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
String Theory ◽  
Lower Bound ◽  
Weak Coupling ◽  
Magnetic Monopoles ◽  
Elementary Particles ◽  
Heterotic String ◽  
Dimensional Torus ◽  
Duality Transformation ◽  
Heterotic String Theory ◽  
Elementary String

We show that in heterotic string theory compactified on a six-dimensional torus, the lower bound (Bogomol’nyi bound) on the dyon mass is invariant under the SL (2, ℤ) transformation that interchanges strong and weak coupling limits of the theory. Elementary string excitations are also shown to satisfy this lower bound. Finally, we identify specific monopole solutions that are related via the strong-weak coupling duality transformation to some of the elementary particles saturating the Bogomol’nyi bound, and these monopoles are shown to have the same mass and degeneracy of states as the corresponding elementary particles.

scholarly journals On the homotopy theory of monoids

1989 ◽  
Vol 47 (2) ◽  
pp. 171-185
Author(s):  
Carol M. Hurwitz
Keyword(s):  
Homotopy Type ◽  
Homotopy Theory ◽  
Small Category ◽  
Homotopy Equivalence ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Finitely Presented

AbsractIn this paper, it is shown that any connected, small category can be embedded in a semi-groupoid (a category in which there is at least one isomorphism between any two elements) in such a way that the embedding includes a homotopy equivalence of classifying spaces. This immediately gives a monoid whose classifying space is of the same homotopy type as that of the small category. This construction is essentially algorithmic, and furthermore, yields a finitely presented monoid whenever the small category is finitely presented. Some of these results are generalizations of ideas of McDuff.

Function spaces related to gauge groups

1992 ◽  
Vol 121 (1-2) ◽  
pp. 185-190 ◽  
Author(s):  
W. A. Sutherland
Keyword(s):  
Topological Group ◽  
Riemann Surface ◽  
Function Space ◽  
Homotopy Type ◽  
Unitary Group ◽  
Function Spaces ◽  
Classifying Space ◽  
Gauge Groups ◽  
Product Method ◽  
Closed Riemann Surface

SynopsisComponents in the function space of maps from a space X to the classifying space BG of a topological group G can sometimes be distinguished up to homotopy type by a Samelson product method. When X is a closed Riemann surface and G is a unitary group, this method is nearly sufficient to classify the components up to homotopy type.

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