scholarly journals Manifolds Homotopy Equivalent to Certain Torus Bundles over Lens Spaces

2020 ◽  
Author(s):  
James F. Davis ◽  
Wolfgang Lück
Keyword(s):  
Homotopy Equivalent ◽  
Lens Spaces ◽  
Torus Bundles

scholarly journals On the Witten–Reshetikhin–Turaev invariants of torus bundles

2015 ◽  
Vol 24 (11) ◽  
pp. 1550055
Author(s):  
Jørgen Ellegaard Andersen ◽  
Søren Fuglede Jørgensen
Keyword(s):  
Growth Rate ◽  
Asymptotic Expansion ◽  
Semiclassical Approximation ◽  
Lens Spaces ◽  
Commun Math Phys ◽  
Torus Bundles ◽  
Mapping Tori ◽  
Chern Simons ◽  
Math Phys

By methods similar to those used by L. Jeffrey [L. C. Jeffrey, Chern–Simons–Witten invariants of lens spaces and torus bundles, and the semiclassical approximation, Commun. Math. Phys.147 (1992) 563–604], we compute the quantum SU (N)-invariants for mapping tori of trace 2 homeomorphisms of a genus 1 surface when N = 2, 3 and discuss their asymptotics. In particular, we obtain directly a proof of a version of Witten's asymptotic expansion conjecture for these 3-manifolds. We further prove the growth rate conjecture for these 3-manifolds in the SU(2) case, where we also allow the 3-manifolds to contain certain knots. In this case we also discuss trace -2 homeomorphisms, obtaining — in combination with Jeffrey's results — a proof of the asymptotic expansion conjecture for all torus bundles.

Isometry classes of 3 dimensional lens spaces

2002 ◽  
Vol 13 (7) ◽  
pp. 295-299
Author(s):  
Michel Cahen ◽  
Mohamed Chaibi
Keyword(s):  
Lens Spaces ◽  
3 Dimensional

scholarly journals TOPOLOGICAL 4-MANIFOLDS WITH 4-DIMENSIONAL FUNDAMENTAL GROUP

2021 ◽  
pp. 1-8
Author(s):  
DANIEL KASPROWSKI ◽  
MARKUS LAND
Keyword(s):  
Fundamental Group ◽  
Homotopy Equivalent ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Canonical Map ◽  
Duality Space ◽  
Simply Connected Manifolds ◽  
Simply Connected ◽  
Poincaré Duality Space

Abstract Let $\pi$ be a group satisfying the Farrell–Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$ has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby–Siebenmann invariant. If $\pi$ is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby–Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel’s conjecture, and simply connected manifolds where rigidity is a consequence of Freedman’s classification results.

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.

On the cohomology of orbit space of free ℤ p -actions on lens spaces

2007 ◽  
Vol 117 (3) ◽  
pp. 287-292 ◽  
Author(s):  
Hemant Kumar Singh ◽  
Tej Bahadur Singh
Keyword(s):  
Orbit Space ◽  
Lens Spaces
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