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A compact manifold is called Bieberbach if it carries a flat Riemannian metric. Bieberbach manifolds are aspherical, therefore the supremum of their systolic ratio, over the set of Riemannian metrics, is finite by a fundamental result of M. Gromov. We study the optimal systolic ratio of compact $3$ -dimensional orientable Bieberbach manifolds which are not tori, and prove that it cannot be realized by a flat metric. We also highlight a metric that we construct on one type of such manifolds ( $C_{2}$ ) which...

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The side-pairing elements of Maskit's fundamental domain for the modular group in genus two.

The Signature of Quasi-Nilpotent Fiber Bundles

The size of triangulations supporting a given link.

The skein polynomial of periodic knots.

The SL(2, C) - character varieties of torus knots.

The SL(2,C) character variety of a class of torus knots.

The slicing number of a knot.

The smallest hyperbolic 6-manifolds.

The space of Surface group representations.

The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on $S^{1} \times B^{3}$ .

The superpolynomial for knot homologies.

The surjectivity problem for one-generator, one-relator extensions of torsion-free groups.

The symmetry of intersection numbers in group theory.

The systolic constant of orientable Bieberbach 3-manifolds

The Three Big Theorems of Papakyriakopoulos

The Tits alternative for $Out (F_{n})$ . I: Dynamics of exponentially-growing automorphisms.

The topological Hawaiian earring group does not embed in the inverse limit of free groups.

The topology of deformation spaces of Kleinian groups.

The topology of the relative character varieties of a quadruply-punctured sphere.

The universal order one invariant of framed knots in most $S^{1}$ -bundles over orientable surfaces.

Currently displaying 121 – 140 of 202