Related papers: Equivariant maps between sphere bundles over tori …

We generalise the Kreck-Stolz invariants s_2 and s_3 by defining a new invariant, the t-invariant, for quaternionic line bundles E over closed spin-manifolds M of dimension 4k-1 with H^3(M; \Q) = 0 such that c_2(E)\in H^4(M) is torsion. The…

We show that the mod 2 Seiberg-Witten invariant can be determined for a spin manifold X which has the same homology groups as the 4-torus. The value depends on the structure of the cohomology ring of X, and in particular on the 4-fold cup…

We show how the families Seiberg-Witten invariants of a family of smooth $4$-manifolds can be recovered from the families Bauer-Furuta invariant via a cohomological formula. We use this formula to deduce several properties of the families…

We construct covariant coordinate transformations on the fuzzy sphere and utilize these to construct a covariant map from a gauge theory on the fuzzy sphere to a gauge theory on the ordinary sphere. We show that this construction coincides…

By using the gluing formulae of the Seiberg-Witten invariant, we show the nonexistence of Einstein metric on manifolds obtained from a 4-manifold with nontrivial Seiberg-Witten invariant by performing sufficiently many connected sums or…

We consider the moduli space of flat $SO(2n+1)$-connections (up to gauge transformations) on a Riemann surface, with fixed holonomy around a marked point. There are natural line bundles over this moduli space; we construct geometric…

We give an algebro-geometric derivation of the known intersection theory on the moduli space of stable rank 2 bundles of odd degree over a smooth curve of genus g. We lift the computation from the moduli space to a Quot scheme, where we…

We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Froyshov's correction term in this setting is an integer-valued invariant of homology cobordism whose…

The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the signature of the associated hermitian form. In this article, this theorem is generalized to…

We introduce and analyse a new type of quantum 2-spheres. Then we apply index theory for noncommutative line bundles over these spheres to conclude that quantum lens spaces are non-crossed-product examples of principal extensions of…

In this paper, we extend the T-duality Hori maps in [arXiv:hep-th/0306062], inducing isomorphisms of twisted cohomologies on T-dual circle bundles, to graded Hori maps and show that they induce isomorphisms of two-variable series of twisted…

We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section…

We show that isomorphism classes $[\mathcal{A}]$ of flat $q\times q$ matrix bundles $\mathcal{A}$ (or projectively flat rank-$q$ complex vector bundles $\mathcal{E}$) on a pro-torus $\mathbb{T}$ are in bijective correspondence with the…

In this paper we give an explicit parametrisation of the moduli space of equivariant harmonic maps from a 2-torus to the 3-sphere. As Hitchin proved, a harmonic map of a 2-torus is described by its spectral data, which consists of a…

We exhaustively classify topological equivariant complex vector bundles over two-sphere under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most)…

Higgs bundles over a closed orientable surface can be defined for any real reductive Lie group G. In this paper we examine the case G=SO*(2n). We describe a rigidity phenomenon encountered in the case of maximal Toledo invariant. Using this…

We define the Toledo invariant of a G-Higgs bundle on a Riemann surface, where G is a real semisimple group of Hermitian type, and we prove a Milnor-Wood type bound for this invariant when the bundle is semistable. We prove rigidity results…

We prove the first inverse theorem for point--sphere incidence bounds over finite fields in dimensions $d \ge 3$, showing that near-extremality forces algebraic rigidity. While sharp upper bounds have been known for over a decade, the…

We study the problem of defining line bundles over certain non-Hausdorff spaces known as Quantum Tori, motivated by the proposed theory of Real Multiplication for real quadratic fields. We draw analogies from the theory of Line Bundles over…

On negatively curved compact manifolds, it is possible to associate to every closed form a bounded cocycle - hence a bounded cohomology class - via integration over straight simplices. The kernel of this map is contained in the space of…