Let Σg be a closed, orientable, connected surface of genus g ≥ 1. The mapping class group Mod(Σg) is the group Homeo(Σg)/Homeo0(Σg) of isotopy classes of orientation-preserving homeomorphisms of Σg. It has been a recurring theme to compare the group Mod(Σg) and its action on the Teichmüller space T (Σg) to lattices in simple Lie groups and their actions on the associated symmetric spaces. Indee...

Let Σg,p be a closed oriented surface of genus g ≥ 1 with p punctures. Let Mod(Σg,p) be the mapping class group of Σg,p. Wajnryb proved in [Wa] that for p = 0, 1 Mod(Σg,p) is generated by two elements. Korkmaz proved in [Ko] that one of these generators can be taken as a Dehn twist. For p ≥ 2, We proved that Mod(Σg,p) is generated by three elements.

For any closed oriented surface Σg of genus g ≥ 3, we prove the existence of foliated Σg-bundles over surfaces such that the signatures of the total spaces are non-zero. We can arrange that the total holonomy of the horizontal foliations preserve a prescribed symplectic form ω on the fiber. We relate the cohomology class represented by the transverse symplectic form to a crossed homomorphism F̃l...

Let Σg be a closed orientable surface of genus g. The mapping class group Modg of Σg is defined to be the group of isotopy classes of orientationpreserving diffeomorphisms Σg → Σg. Recall that an essential simple closed curve γ in Σg is called a bounding curve, or separating curve, if it is nullhomologous in Σg or, equivalently, if γ separates Σg into two connected components. Let Kg denote the...

6229 lines of the Ballik-Ramsay system (b(3)Σg (-)-a(3)Πu) and the Phillips system (A(1)Πu-X(1)Σg (+)) of C2 up to v = 8 and J = 76, which were taken from the literature or assigned in the present work, were analyzed simultaneously by least-squares fitting with 82 Dunham-like molecular parameters and spin-orbit interaction constants between the b(3)Σg (-) and X(1)Σg (+) states with a standard d...

We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S. We determine HF(Σg × S, s;C) completely in the case c1(s) = 0, which for g ≥ 3 was previously unknown. We show that in this case HF∞ is closely related to the cohomology of a the total space of a certain circle bundle over the Jacobian torus of Σg, and furthermore that HF(Σg ×S, s;Z)...

Let Σg,b denote a closed orientable surface of genus g with b punctures and let Mod(Σg,b) denote its mapping class group. In [Luo] Luo proved that if the genus is at least 3, Mod(Σg,b) is generated by involutions. He also asked if there exists a universal upper bound, independent of genus and the number of punctures, for the number of torsion elements/involutions needed to generate Mod(Σg,b). B...

Accurate absolute level energies of the B Σu , v = 0− 8, N and EF Σg , v = 0 − 21, N rovibrational quantum states of molecular deuterium are derived by combining results from a Doppler-free two-photon laser excitation study on several lines in the EF Σg −X Σg (0,0) band, with results from a Fourier-transform spectroscopic emission study on a low-pressure hydrogen discharge. Level energy uncerta...

We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S . We determine HF(Σg × S , s;C) completely in the case c1(s) = 0, which for g ≥ 3 was previously unknown. We show that in this case HF∞ is closely related to the cohomology of a the total space of a certain circle bundle over the Jacobian torus of Σg, and furthermore that HF (Σg ×S , ...

Let Σg be a closed orientable surface of genus g. The mapping class group Modg of Σg is defined to be the group of isotopy classes of orientationpreserving diffeomorphisms Σg → Σg. Recall that an essential simple closed curve γ in Σg is called a bounding curve, or separating curve, if it is nullhomologous in Σg or, equivalently, if γ separates Σg into two connected components. Let Kg denote the...