Related papers: A 3-skeleton for a classifying space for the symme…

We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties are investigated. We are mainly concentrated on integral…

For N=5, 6 and 7, using the classification of perfect quadratic forms, we compute the homology of the Voronoi cell complexes attached to the modular groups SL_N(\Z) and GL_N(\Z). From this we deduce the rational cohomology of those groups.

A brane in a symplectic manifold is a coisotropic submanifold $Y$ endowed with a compatible closed 2-form $F$, which together induce a transverse complex structure. For a specific class of branes we give an explicit description of branes…

We apply mapping class group techniques and trisections to study intersection forms of smooth 4-manifolds. Johnson defined a well-known homomorphism from the Torelli group of a compact surface. Morita later showed that every homology…

We present the subalgebra structure of sl(3,O), a particular real form of e6 chosen for its relevance to particle physics and its close relation to generalized Lorentz groups. We use an explicit representation of the Lie group SL(3,O) to…

We study the moduli space of solutions to the Seiberg-Witten equations with $N$ spinors on a compact Riemann surface. These moduli spaces arise in a program to define a new enumerative invariant of 3-manifolds. They are also of independent…

We consider compact homogeneous spaces G/H of positive Euler characteristic endowed with an invariant almost complex structure J and the canonical action \theta of the maximal torus T ^{k} on G/H. We obtain explicit formula for the…

We present a geometric construction of a new class of hyper-Kahler manifolds with torsion. This involves the superposition of the four-dimensional hyper-Kahler geometry with torsion associated with the NS-5-brane along quaternionic planes…

We introduce a notion of lexicographic shellability for pure, balanced boolean cell complexes, modelled after the $CL$-shellability criterion of Bj\"orner and Wachs for posets and its generalization by Kozlov called $CC$-shellability. We…

We give a concrete method to explicitly compute the rational cohomology of the unordered configuration spaces of connected, oriented, closed, even-dimensional manifolds of finite type which we have implemented in Sage [S+09]. As an…

The Kauffman bracket skein modules, S(M,A), have been calculated for A=+1,-1, for all 3-manifolds M by relating them to the SL(2,C)-character varieties. We extend this description to the case when A is a 4-th root of 1 and M is either a…

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…

An invariant of orientable 3-manifolds is defined by taking the minimum $n$ such that a given 3-manifold embeds in the connected sum of $n$ copies of $S^2 \times S^2$, and we call this $n$ the embedding number of the 3-manifold. We give…

Heegaard splittings provide a natural representation of closed 3-manifolds by gluing two handlebodies along a common surface. These splittings can be equivalently given by two finite sets of meridians lying on the surface, which define a…

We conclude the construction of the algebraic complex, consisting of spaces of differentials of Euclidean metric values, for four-dimensional piecewise-linear manifolds. Assuming that the complex is acyclic, we investigate how its torsion…

Various properties of a class of braid matrices, presented before, are studied considering $N^2 \times N^2 (N=3,4,...)$ vector representations for two subclasses. For $q=1$ the matrices are nontrivial. Triangularity $(\hat R^2 =I)$…

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\omega_4$ of $G$'s cohomology group…

In this paper, we make use of the relations between the braid and mapping class groups of a compact, connected, non-orientable surface N without boundary and those of its orientable double covering S to study embeddings of these groups and…

We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter…

This is a summary of the work in the author's recent paper with this title written with Jerome Gauntlett, George Papadopoulos and Paul Townsend, hep-th/9702202. We showed how to construct hyper-K\"ahler 8-metrics in terms of arrangements of…