Related papers: Seiberg-Witten invariants and surface singularitie…

For a connected Lie group G, we show that a complex structure on the total space TG of the tangent bundle of G that is left invariant and has the property that each left translation G-orbit is a totally real submanifold is induced from a…

In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…

For any negative definite plumbed 3-manifold M we construct from its plumbed graph a graded Z[U]-module. This, for rational homology spheres, conjecturally equals the Heegaard-Floer homology of Ozsvath and Szabo, but it has even more…

We prove the Gersten conjecture for $p$-adic \'etale Tate twists for a smooth scheme $X$ in mixed characteristic in the Nisnevich topology. Our main observation is that, while $p$-adic \'etale Tate twists are not $\mathbb A^1$-invariant,…

We revisit three results due to Morita expressing certain natural integral cohomology classes on the universal family of Riemann surfaces C_g, coming from the parallel symplectic form on the universal jacobian, in terms of the…

We define higher genus Gromov-Witten invariants and establish a mathematical theory of sigma model coupled with gravity over any semi-positive symplectic manifolds. As applications, we verify the stablizing conjecture of symplectic…

We present a short proof of the gauge invariant uniqueness theorem for relative Cuntz-Pimsner algebras of C*-correspondences.

In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The…

In this article, we give a general construction of spectral triples from certain Lie group actions on unital C*-algebras. If the group G is compact and the action is ergodic, we actually obtain a real and finitely summable spectral triple…

Fintushel and Stern have proved that if S \subset X is a symplectic surface in a symplectic 4-manifold such that S has simply-connected complement and nonnegative self-intersection, then there are infinitely many topologically equivalent…

In this paper we use the Morse theory of the Yang-Mills-Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2,1) and SU(2,1) Higgs bundles with fixed…

We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants…

The symplectic derivation Lie algebras defined by Kontsevich are related to various geometric objects including moduli spaces of graphs and of Riemann surfaces, graph homologies, Hamiltonian vector fields, etc. Each of them and its…

We study invariant Seifert surfaces for strongly invertible knots, and prove that the gap between the equivariant genus (the minimum of the genera of invariant Seifert surfaces) of a strongly invertible knot and the (usual) genus of the…

While the topological types of {normal} surface singularities with homology sphere link have been classified, forming a rich class, until recently little was known about the possible analytic structures. We proved in [Geom. Topol. 9(2005)…

In this paper, we investigate structural properties of finite groups that are detected by certain group invariants arising from Dijkgraaf--Witten theory, a topological quantum field theory, in one space and one time dimension. In this…

We propose two conjectural relationships between the equivariant Gromov-Witten invariants of the resolved conifold under diagonal and anti-diagonal actions and the Gromov-Witten invariants of $\mathbb{P}^1$, and verify their validity in…

The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge theories, and allows to express the noncommutative variables in terms of the commutative ones. Its explicit form can be found order by order in the noncommutative…

We recover the Newton diagram (modulo a natural ambiguity) from the link for any surface hypersurface singularity with non-degenerate Newton principal part whose link is a rational homology sphere. As a corollary, we show that the link…

We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures, when G is a real reductive Lie group, and establish a correspondence between these objects and representations of the fundamental group of the punctured…