Related papers: Relations on Mbar_{g,n} via 3-spin structures
The moduli space of stable relative maps to the projective line combines features of stable maps and admissible covers. We prove all standard Gromov-Witten classes on these moduli spaces of stable relative maps have tautological…
After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, we explain three methods of detecting non-tautological classes in cohomology. The first…
In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof…
We define the notion of Witt structure on the tangent bundle of a pseudo-Riemannian manifold and we introduce a connection adapted to a such structure. The notions of geodesics and symmetric spaces are revisited in this setting and…
Let $M_g$ be the moduli space of smooth genus $g$ curves. We define a notion of Chow groups of $M_g$ with coefficients in a representation of $Sp(2g)$, and we define a subgroup of tautological classes in these Chow groups with twisted…
We study tautological classes on the moduli space of stable $n$-pointed hyperelliptic curves of genus $g$ with rational tails. Our result gives a complete description of tautological relations. The method is based on the approach of Yin in…
We show that the non-commutative $CP^1$ model coupled with Hopf term in 3 dimensions is equivalent to an interacting spin-$s$ theory where the spin $s$ of the dual theory is related to the coefficient of the Hopf term. We use the…
We construct a compact minitwistor space from a hyperelliptic curve with real structure and show that it yields a lot of new Lorentzian Einstein-Weyl spaces all of which are diffeomorphic to the 3-dimensional deSitter space. These…
We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres-Douglas theories on $S^1 \times M_3$ with a non-trivial holonomy of a discrete global symmetry along the $S^1$.…
Let $G$ be a compact connected semisimple Lie group. We extend the techniques of Weinstein [W] to give a construction in group cohomology of symplectic forms $\omega$ on \lq twisted' moduli spaces of representations of the fundamental group…
For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…
The quasiclassical theory in terms of equations for the Green's functions (Eilenberger equations) is generalized in order to allow for quantitative description of the magneto-electric effects and proximity-induced triplet correlations in…
We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset U(V)$ is a compact Lie group containing $-id_V$. We study and classify $Spin^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations associated with…
Recently the long-standing puzzle about counting the Witten index in N=1 supersymmetric gauge theories was resolved. The resolution was based on existence (for higher orthogonal $SO(N), N \geq 7$ and exceptional gauge groups) of flat…
The virtual geometry of the moduli space of stable quotients is used to obtain Chow relations among the kappa classes on the moduli space of nonsingular genus g curves. In a series of steps, the stable quotient relations are rewritten in…
The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of…
We provide a differential cocycle model for elliptic cohomology with complex coefficients and use analytic methods to construct a cocycle representative for the Witten class in this language. Our motivation stems from the conjectural…
We introduce W-spin structures on a Riemann surface and give a precise definition to the corresponding W-spin equations for any quasi-homogeneous polynomial W. Then, we construct examples of nonzero solutions of spin equations in the…
In this work, we study topological properties of surface bundles, with an emphasis on surface bundles with a spin structure. We develop a criterion to decide whether a given manifold bundle has a spin structure and specialize it to surface…
We define the logarithmic tautological rings of the moduli spaces of Deligne-Mumford stable curves (together with a set of additive generators lifting the decorated strata classes of the standard tautological rings). While these algebras…