Topological gauge theories and group cohomology

We show that three dimensional Chern-Simons gauge theories with a compact gauge groupG (not necessarily connected or simply connected) can be classified by the integer cohomology groupH ⁴(BG,Z). In a similar way, possible Wess-Zumino interactions of such a groupG are classified byH ³(G,Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map fromH ⁴(BG,Z) toH ³(G,Z). We generalize this correspondence to topological spin theories, which are defined on three manifolds with spin structure, and are related to what might be calledZ ₂ graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.     

C=1 conformal field theories on Riemann surfaces

We study the theory ofc=1 torus and ₂-orbifold models on general Riemann surfaces. The operator content and occurrence of multi-critical points in this class of theories is discussed. The partition functions and correlation functions of vertex operators and twist fields are calculated using the theory of double covered Riemann surfaces. It is shown that orbifold partition functions are sensitive to the Torelli group. We give an algebraic construction of the operator formulation of these nonchiral theories on higher genus surfaces. Modular transformations are naturally incorporated as canonical transformations in the Hilbert space.     

Synthesis and characterization of iPP‐sPP stereoblock produced by a binary metallocene system

Stereoblock polypropylenes comprising of iPP and sPP segments are synthesized by polymerization of the following binary system of metallocenes: the C_s‐symmetric [2,7‐t‐Bu₂(Flu)₂Ph₂C(Cp)ZrCl₂] and the C₂‐symmetric rac‐Me₂Si(2‐Me‐4‐Ph‐Ind)₂ZrCl₂. Blends of samples made either by each catalyst individually (solution blend) with materials obtained with the mixed catalyst system (reactor blend) are compared. The simultaneous presence of MAO and DEZ, enhancing fast and reversible transfer of the growing chains between the two active centers, leads to the formation of a stereoblock microstructure. In this case, low molecular weight polymers are obtained. The junction between the blocks is qualitatively observed in ¹³C NMR. When made in toluene, the stereoblock material consists of a majority of syndiotactic sequences, whereas the ratio is more equilibrated when the polymerization was conducted in the more polar chlorobenzene. This is confirmed by the results obtained with ¹³C NMR, CRYSTAF, HT HPLC, DSC, SSA, WAXD, and optical microscopy. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1422–1434     

An addition theorem for the color number

There is a close relation between the color number of a continuous map without fixed points and the topological dimension. If  is an involution, the color number is also related to the co-index. An addition theorem for the color number is established thus underscoring the interrelations between color number, dimension and co-index.

     

The volume conjecture,perturbative knot invariants,and recursion relations for topological strings

We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C)$\mathit{SL}(2;\mathbb{C})$ Chern–Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard–Orantin topological recursion relation. We discuss the correspondence for the figure eight knot complement and the once punctured torus bundle over S¹${\mathbb{S}}^1$ with the monodromy L²R$L^{2}R$ up to the fifth order. For the torus knots, we find trivial the recursion relations on both sides.     

Matrix string theory

Via compactification on a circle, the matrix mode] of M-theory proposed by Banks et a]. suggests a concrete identification between the large N limit of two-dimensional N = 8 supersymmetric Yang-Mills theory and type IIA string theory. In this paper we collect evidence that supports this identification. We explicitly identify the perturbative string states and their interactions, and describe the appearance of D-particle and D-membrane states.     

Non-Pincer-Type Manganese Complexes as Efficient Catalysts for the Hydrogenation of Esters

Catalytic hydrogenation of carboxylic acid esters is essential for the green production of pharmaceuticals, fragrances, and fine chemicals. Herein, we report the efficient hydrogenation of esters with manganese catalysts based on simple bidentate aminophosphine ligands. Monoligated Mn PN complexes are particularly active for the conversion of esters into the corresponding alcohols at Mn concentrations as low as 0.2 mol % in the presence of sub-stoichiometric amounts of KO^tBu base.     

Balanced Topological Field Theories

We describe a class of topological field theories called “balanced topological field theories”. These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of “iterated superspaces” that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space. Received: 2 September 1996 / Accepted: 3 October 1996