970 research outputs found
Some hyperbolic 4-manifolds with low volume and number of cusps
No full textWe construct here two new examples of non-orientable, non-compact, hyperbolic 4-manifolds. The first has minimal volume v m = 4π 2 /3 and two cusps. This example has the lowest number of cusps among known minimal volume hyperbolic
4-manifolds. The second has volume 2 ·v m and one cusp. It has lowest volume among known one-cusped hyperbolic 4-manifolds
The complement of the figure-eight knot geometrically bounds
No full textWe show that some hyperbolic 3-manifolds which are tessellated
by copies of the regular ideal hyperbolic tetrahedron are geodesically embedded
in a complete, finite volume, hyperbolic 4-manifold. This allows us to prove
that the complement of the figure-eight knot geometrically bounds a complete,
finite volume hyperbolic 4-manifold. This is the first example of geometri-
cally bounding hyperbolic knot complements and, amongst known examples
of geometrically bounding manifolds, the one with the smallest volume
New hyperbolic 4–manifolds of low volume
No full textWe prove that there are at least two commensurability classes of (cusped, arithmetic)
minimal-volume hyperbolic 4–manifolds. Moreover, by applying a well-known
technique due to Gromov and Piatetski-Shapiro, we build the smallest known non-
arithmetic hyperbolic 4–manifold
Cusps of hyperbolic 4‐manifolds and rational homology spheres
No full textIn the present paper, we construct a cusped hyperbolic 4-manifold with all cusp sections
homeomorphic to the Hantzsche–Wendt manifold, which is a rational homology sphere. By a
result of Golénia and Moroianu, the Laplacian on 2-forms on such a manifold has purely discrete
spectrum. This shows that one of the main results of Mazzeo and Phillips from 1990 cannot hold
without additional assumptions on the homology of the cusps. This also answers a question by
Golénia and Moroianu from 2012.
We also correct and refine the incomplete classification of compact orientable flat 3-manifolds
arising from cube colourings provided earlier by the last two authors
Embedding arithmetic hyperbolic manifolds
No full textWe prove that any arithmetic hyperbolic n-manifold of simplest
type can either be geodesically embedded into an arithmetic hyper-
bolic (n + 1)-manifold or its universal mod 2 Abelian cover can
Convex plumbings in closed hyperbolic 4-manifolds
No full textWe show that every plumbing of disc bundles over surfaces whose genera satisfy a simple inequality may be embedded as a convex submanifold in some closed hyperbolic four-manifold. In particular its interior has a geometrically finite hyperbolic structure that covers a closed hyperbolic four-manifold
Compact hyperbolic manifolds without spin structures
No full textWe exhibit the first examples of compact, orientable, hyperbolic manifolds that do not have any spin structure. We show that such manifolds exist in all dimensions
n≥4. The core of the argument is the construction of a compact, oriented, hyperbolic 4–manifold M that contains a surface S of genus 3 with self-intersection 1. The 4–manifold M
has an odd intersection form and is hence not spin. It is built by carefully assembling some right-angled 120–cells along a pattern inspired by the minimum trisection of CP2
.The manifold M is also the first example of a compact, orientable, hyperbolic 4–manifold satisfying either of these conditions:
1) H2(M,Z) is not generated by geodesically immersed surfaces.
2)There is a covering M that is a nontrivial bundle over a compact surface
Embedding non-arithmetic hyperbolic manifolds
No full textThis paper shows that many hyperbolic manifolds obtained by glueing
arithmetic pieces embed into higher-dimensional hyperbolic manifolds as
codimension-one totally geodesic submanifolds. As a consequence, many
Gromov--Pyatetski-Shapiro and Agol--Belolipetsky--Thomson non-arithmetic
manifolds embed geodesically. Moreover, we show that the number of
commensurability classes of hyperbolic manifolds with a representative of
volume that bounds geometrically is at least , for large
enough.Comment: 20 pages, 5 figures. Final versio
Returning culture to peacebuilding : contesting the liberal peace in Sierra Leone
No full textThis thesis investigates the advantages and limitations of applying culture to the analysis of violent conflict and peacebuilding, with a particular focus on liberal peacebuilding in Sierra Leone. While fully aware of the critique of the concept of culture in terms of its uses for the production of difference and ‘otherness,’ it also seeks to respond to the critique of liberal peacebuilding on the account of its low sensitivity towards local culture, which allegedly undermines the peace effort. After a careful examination of the terms of discussion about culture enabled by theoretical approaches to conflict in Chapter 2, the thesis presents a theoretical framework for the analysis of cultural aspects of conflict and peace based on the processes and effects of meaning-generation (Chapter 3), developing the conceptual apparatus and vocabulary for the subsequent empirical study. Instead of bracketing out the recursive nature of cultural theorising, the developed approach embraces the recursive dynamics which arise as a result of cultural ‘embeddedness’ of the analyst and the processes which s/he seeks to elucidate, mirroring similar dynamics in the cultural production of meaning and knowledge. The framework of ‘embedded cultural enquiry’ is then used to analyse the practices of liberal peacebuilding as a particular culture, which shapes the interaction of the liberal peace with its ‘subjects’ and critics as well as framing its reception of the cultural problematic generally (Chapter 4). The application of the analytical framework to the case study investigates the interaction between the liberal peace and ‘local culture,’ offering an alternative reading of the conflict and peace process in Sierra Leone (Chapter 5). The study concludes that a greater attention to cultural meaning-making offers a largely untapped potential for peacebuilding, although any decisions with regard to its deployment will inevitably be made from within an inherently biased cultural perspective
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