Related papers: Spin structures on the Seiberg-Witten moduli space…

In the present thesis we study the geometry of the moduli spaces of Bradlow-Higgs triples on a smooth projective curve $C$. $(E,\varphi, s)$ is a Bradlow-Higgs triple if $(E,\varphi)$ is a Higgs bundle and $s$ is a non-zero global section…

The set of unrestricted homotopy classes $[M,S^n]$ where $M$ is a closed and connected spin $(n+1)$-manifold is called the $n$-th cohomotopy group $\pi^n(M)$ of $M$. Moreover it is known that $\pi^n(M) = H^n(M;\mathbb Z) \oplus \mathbb Z_2$…

We show that the periodic $\eta$-invariants introduced by Mrowka--Ruberman--Saveliev~\cite{MRS3} provide obstructions to the existence of cobordisms with positive scalar curvature metrics between manifolds of dimensions $4$ and $6$. The…

We introduce and study equivariant Seiberg-Witten invariants for $4$-manifolds equipped with a smooth action of a finite group $G$. Our invariants come in two types: cohomological, valued in the group cohomology of $G$ and $K$-theoretic,…

Motivated by a variant of Atiyah-Floer conjecture proposed in \cite{L2} and its potential generalizations, we study in this article and its sequel as a first step properties of moduli spaces of Seiberg-Witten equations on a 3-dimensional…

It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…

We prove that any connected component of the space of m-spin structures on compact Riemann surfaces with finite number of punctures and holes is homeomorphic to a quotient of the vector space R^d by a discrete group action. Our proof is…

We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the first classes of manifolds for which these moduli spaces have…

The main result of this paper is the construction of a family of superintegrable Hamiltonian systems on moduli spaces of flat connections on a principle $G$-bundle on a surface. The moduli space is a Poisson variety with Atiyah-Bott Poisson…

Let $(M,g)$ be a pseudo-Riemannian manifold of signature $(p,q)$. We compute the obstruction for a vector bundle $S$ over $(M,g)$ to admit a Dirac operator whose principal symbol induces on $S$ the structure of a bundle of irreducible real…

We show that the moduli space of nonnegatively curved metrics on each member of a large class of 2-connected 7-manifolds, including each smooth manifold homeomorphic to $S^7$, has infinitely many connected components. The components are…

We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderson's conjecture in a strong sense, showing that the map from…

A spin system is a sequence of self-adjoint unitary operators $U_1,U_2,...$ acting on a Hilbert space $H$ which either commute or anticommute, $U_iU_j=\pm U_jU_i$ for all $i,j$; it is is called irreducible when $\{U_1,U_2,...\}$ is an…

We study the dependence of the eta invariant $\eta_D$ on the spin structure, where $D$ is a twisted Dirac operator on a (4k+3)-dimensional spin manifold. The difference between the eta invariants for two spin structures related by a…

We prove a rigidity result for automorphisms of points of certain stacks admitting adequate moduli spaces. It encompasses as special cases variations of the moduli of $G$-bundles on a smooth projective curve for a reductive algebraic group…

We develop a version of Seiberg--Witten Floer cohomology/homotopy type for a spin$^c$ 4-manifold with boundary and with an involution which reverses the spin$^c$ structure, as well as a version of Floer cohomology/homotopy type for oriented…

In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space $M_\Sigma$ with singular stratum $\beta M$ (a closed manifold of positive codimension) and associated link equal to…

We consider Riemannian 4-manifolds $(X,g_X)$ with a Spin^c-structure and a suitable circle bundle $Y$ over $X$ such that the Spin^c-structure on $X$ lifts to a spin structure on $Y$. With respect to these structures a spinor $\phi$ on $X$…

The aim of this paper is to determine a bound of the dimension of an irreducible component of the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces. Let $X$ be a non-singular irreducible complex surface and let $E$ be a…

We construct F-structures on a Bott manifold and on some other manifolds obtained by Kummer-type constructions. We also prove that if M=E#X, where E is a fiber bundle with structure group G and a fiber admitting a G-invariant metric of…