Related papers: Relations on Mbar_{g,n} via 3-spin structures

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…

In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…

We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string…

The rational cohomology of the moduli space of rank two, odd degree stable bundles over a curve (of genus g > 1) has been studied intensely in recent years and in particular the invariant subring generated by Newstead's generators alpha,…

Using a simple geometric argument, we obtain an infinite family of nontrivial relations in the tautological ring of $M_g$ (and in fact that of $M_{g,2}$). One immediate consequence of these relations is that the classes…

We employ the $1/2$-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities of kappa-classes on $\mathcal{M}_g$, $g\geq 2$. We…

The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…

Based on the combinatorial description of the moduli spaces of curves provided by Strebel differentials, Witten and Kontsevich have introduced combinatorial cohomology classes $W_{(m_0,m_1,m_2,\dots),n}$, and conjectured that these can be…

The dth symmetric product of a curve of genus g is a smooth projective variety. This paper is concerned with the little quantum cohomology ring of this variety, that is, the ring having its 3-point Gromov-Witten invariants as structure…

Witten established correspondence between multiparton amplitudes in four-dimensional maximally supersymmetric gauge theory and topological string theory on supertwistor space $CP^{3|4}$. We extend Witten's correspondence to gauge theories…

We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…

We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus $g$ with $n$ marked points. A large part of these relations has a surprisingly simple form: the…

We study the higher genus equivariant Gromov-Witten theory of the Hilbert scheme of n points of the plane. Since the equivariant quantum cohomology is semisimple, the higher genus theory is determined by an R-matrix via the Givental-Teleman…

It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by…

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum $sl(2)$ were obtained by the last three authors in arXiv:1202.3553 . They are invariants of $3$-manifolds together with a cohomology class which…

In the context of the AdS$_3$/CFT$_2$ correspondence, we investigate the Higgs branch CFT$_2$. Witten showed that states localised near the small instanton singularity can be described in terms of vector multiplet variables. This theory has…

We derive an effective recursion for Witten's r-spin intersection numbers, using Witten's conjecture relating r-spin numbers to the Gel'fand-Dikii hierarchy (Theorem 4.1). Consequences include closed-form descriptions of the intersection…

We discuss 2-cocycles of the Lie algebra $\Map(M^3;\g)$ of smooth, compactly supported maps on 3-dimensional manifolds $M^3$ with values in a compact, semi-simple Lie algebra $\g$. We show by explicit calculation that the…

In [arXiv:1912.02063], we constructed 3-dimensional Topological Quantum Field Theories (TQFTs) using not necessarily semisimple modular categories. Here, we study projective representations of mapping class groups of surfaces defined by…

Gromov-Witten (GW) theory produces Chow and cohomology classes on the moduli of curves, and there are several conjectures/speculations about their relation to the tautological ring. We develop new degeneration techniques to address these.…