scholarly journals On symplectic fillings of virtually overtwisted torus bundles

2021 ◽  
Vol 21 (1) ◽  
pp. 469-505
Author(s):  
Austin Christian
Keyword(s):  
Torus Bundles

Examples for obstructions to action-angle coordinates

1988 ◽  
Vol 110 (1-2) ◽  
pp. 27-30 ◽  
Author(s):  
Larry M. Bates
Keyword(s):  
Global Existence ◽  
Symplectic Manifolds ◽  
Torus Bundles

SynopsisWe give examples of symplectic manifolds which are also non-trivial principal torus-bundles with Lagrangian fibres. These bundles are examples of spaces with an obstruction to the global existence of action-angle variables.

scholarly journals Fintushel-Stern knot surgery in torus bundles

2017 ◽  
Vol 10 (1) ◽  
pp. 164-177
Author(s):  
Yi Ni
Keyword(s):  
Torus Bundles ◽  
Knot Surgery

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.

Profinite genus of fundamental groups of torus bundles

2019 ◽  
Vol 48 (4) ◽  
pp. 1567-1576
Author(s):  
Genildo de Jesus Nery
Keyword(s):  
Fundamental Groups ◽  
Torus Bundles

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.

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