ABSTRACT In this work, we explore the diversity of ionized gas kinematics (rotational velocity vϕ and dispersion σg) gas-phase metallicity gradients at 0.1 ≤ z 2.5 using a compiled data set 74 galaxies resolved with ground-based integral field spectroscopy. We find that highest lowest σg have preferentially flat gradients, whereas those intermediate values show large scatter in gradients. Addit...

Theorem 2. Suppose Σg,n is a compact orientable surface of genus g with n boundary components. Let {a1, ...., a3g−3+2n} be a 3-holed sphere decomposition of the surface where ∂Σg,n = a3g−2+n ∪ ... ∪ a3g−3+2n. Then each orientation preserving homeomorphism of the surface which is the identity map on ∂Σg,n is isotopic to a composition qp where p is positive and q is a composition of negative Dehn...

Let Σg (respectively Σ/J be a closed oriented surface of genus g (respectively h), where g (respectively h) is a non-negative integer. Let Diff+Σh be the group of all orientation-preserving difϊeomorphisms of Σ/j with C°°-topology. A Σ^bundle over Σg (also called a surface bundle over a surface) is fiber bundle ξ = (£", Σg,p, Σ/^Diff+Σfr) over Σ^ with total space E, fiber Σ&, projection p : E —...

We show that there are homeomorphisms of closed oriented genus g surfaces Σg which are fiber-preserving with respect to an irregular branched covering Σg → S2 and isotopic to the identity, but which are not fiber-isotopic to the identity.

Let Σg be an oriented connected real two dimensional manifold of genus g without boundary. For periodic homeomorphisms of Σg that commute with a hyperelliptic involution, we give a method to obtain their presentations by Dehn

Gene expression during spore development in Bacillus subtilis is controlled by cell type-specific RNA polymerase sigma factors. σFand σE control early stages of development in the forespore and the mother cell, respectively. When, at an intermediate stage in development, the mother cell engulfs the forespore, σF is replaced by σG and σE is replaced by σK. The anti-sigma factor CsfB is produced ...

We construct some examples of special Lagrangian submanifolds and Lagrangian self-similar solutions in almost Calabi–Yau cones over toric Sasaki manifolds. For example, for any integer g ≥ 1, we can construct a real 6-dimensional Calabi–Yau cone Mg and a 3-dimensional special Lagrangian submanifold F 1 g : L 1 g → Mg which is diffeomorphic to Σg ×R and a compact Lagrangian self-shrinker F 2 g :...

Recall that the rank of a finitely generated group is the minimal number of elements needed to generate it. M. White [Whi02] has proven that the injectivity radius of M is bounded above by some function of rank(π1(M)). Building on a technique that he introduced, we show that if M is a hyperbolic 3-manifold fibering over the circle with fiber Σg and rank(π1(M)) 6= 2g + 1, then the diameter of M ...

We show the problem of counting homomorphisms from the fundamental group of a homology 3-sphere M to a finite, non-abelian simple group G is #P-complete, in the case that G is fixed and M is the computational input. Similarly, deciding if there is a non-trivial homomorphism is NP-complete. In both reductions, we can guarantee that every non-trivial homomorphism is a surjection. As a corollary, ...

In this paper, we study a series of L-torsion invariants from the viewpoint of the mapping class group of a surface. We establish some vanishing theorems for them. Moreover we explicitly calculate the first two invariants and compare them with hyperbolic volumes. 1. Magnus representation Let Σg,1 be a compact oriented smooth surface of genus g with a boundary ∂Σg,1 ∼= S . In this paper, we alwa...