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Discovery Projects - Grant ID: DP160104502

Title
Discovery Projects - Grant ID: DP160104502
Funding
ARC | Discovery Projects
Contract (GA) number
DP160104502
Start Date
2016/01/01
End Date
2020/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP160104502

 

  • Unravelling the Dodecahedral Spaces

    Spreer, Jonathan; Tillmann, Stephan (2017)
    Projects: ARC | Discovery Projects - Grant ID: DP160104502 (DP160104502)
    The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a very short hierarchy. Moreover, we describe a 60-sheeted cover in which the associated cubulation is special. We also describe the natural cubulation and covers of the spherical do...

    Computing trisections of 4-manifolds

    Bell, Mark; Hass, Joel; Rubinstein, J. Hyam; Tillmann, Stephan (2017)
    Projects: ARC | Discovery Projects - Grant ID: DP160104502 (DP160104502)
    Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to algorithmically construct a trisection, which describes a $4$-dimensional manifold as a union of three $4$-dimensional handlebodies. The complexity of the $4$-manifold is captured in a collection of curves on a surface, which guide the gluing of the handelbodies. The ...

    The trisection genus of standard simply connected PL 4-manifolds

    Spreer, Jonathan; Tillmann, Stephan (2017)
    Projects: ARC | Discovery Projects - Grant ID: DP160104502 (DP160104502)
    Gay and Kirby recently introduced the concept of a trisection for arbitrary smooth, oriented closed 4-manifolds, and with it a new topological invariant, called the trisection genus. In this note we show that the K3 surface has trisection genus 22. This implies that the trisection genus of all standard simply connected PL 4-manifolds is known. We show that the trisection genus of each of these manifolds is realised by a trisection that is supported by a singular triangulation. Moreover, we ex...

    Z2-Thurston Norm and Complexity of 3-Manifolds, II

    In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3--manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we obtain the first infinite families of minimal triangulations of Seifert fibred spaces modelled on Thurston's geometry $\widetilde{\text{SL}_2(\mathbb{R})}.$
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