Related papers: Chern class obstructions to smooth equivariant rig…

In this paper, we provide new examples of 1-obstructed and atomic sheaves on an infinite series of locally complete families of projective hyper-K\"ahler manifolds. More precisely, (1) we prove that the fixed loci of the natural…

Motivated by S-duality modularity conjectures in string theory, we study the Donaldson-Thomas type invariants of pure 2-dimensional sheaves inside a nonsingular threefold X in three different situations: (1). X is a K3 fibration over a…

We prove an analogue for odd dimensional manifolds with boundary, in the $b$-calculus setting, of the higher Atiyah-Patodi-Singer index theorem by Getzler and Wu, thus obtain a natural counterpart of the eta invariant for even dimensional…

We prove an existence theorem for gauge invariant $L^2$-normal neighborhoods of the reduction loci in the space ${\cal A}_a(E)$ of oriented connections on a fixed Hermitian 2-bundle $E$. We use this to obtain results on the topology of the…

We provide new constraints for algebro-geometric subgroups of mapping class groups, namely images of fundamental groups of curves under complex algebraic maps to the moduli space of smooth curves. Specifically, we prove that the restriction…

We extend a construction of Stipsicz-Szab\'{o} of infinitely many irreducible exotic smooth structures of some closed four-manifolds with even $b_2^+$ and fundamental group $\mathbb{Z}/2\mathbb{Z}$. We use the double node surgery and…

We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist.…

In this paper, we investigate existence of inequivalent smooth structures on closed smooth non-orientable 4-manifolds building upon results of Akbulut, Cappell-Shaneson, Fintushel-Stern, Gompf, and Stolz. We add to the number of known…

We introduce smooth atlas stratified spaces. We show that this class is closed under cartesian products; consequently, it is possible to define fiber bundles of smooth atlas stratified spaces. We describe the resolution of such a space to a…

We study the Seiberg-Witten invariant $\lambda_{\rm{SW}} (X)$ of smooth spin $4$-manifolds $X$ with integral homology of $S^1\times S^3$ defined by Mrowka, Ruberman, and Saveliev as a signed count of irreducible monopoles amended by an…

We consider the conormal bundle of a Schubert variety $S_I$ in the cotangent bundle $T^* Gr$ of the Grassmannian $Gr$ of $k$-planes in $C^n$. This conormal bundle has a fundamental class ${\kappa_I}$ in the equivariant cohomology…

Let $X$ be a smooth, compact, oriented $4$-manifold. Building upon work of Li-Liu, Ruberman, Nakamura and Konno, we consider a families version of Seiberg-Witten theory and obtain obstructions to the existence of certain group actions on…

For a symplectic manifold with an anti-symplectic involution having non-empty fixed locus, we construct a model of the moduli space of real sphere maps out of moduli spaces of decorated disk maps and give an explicit expression for its…

We give a construction of the moduli space of stable maps to the classifying stack B\mu_r of a cyclic group by a sequence of r-th root constructions on M_{0, n}. We prove a closed formula for the total Chern class of \mu_r-eigenspaces of…

The invariant integration method for Chern-Simons theory defined on the compact hyperbolic manifold {\Gamma}\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function is presented. We discuss…

Motivated by generalized geometry (in the sense of Hitchin), the product bundle ${\mathcal Z}\times_{M} {\mathcal Z}$ of the twistor space ${\mathcal Z}$ of a Riemannian manifold $(M,g)$ is considered. The product twistor space admits a…

The self-dual Einstein equations on a compact Riemannian 4-manifold can be expressed as a quadratic condition on the curvature of an $SU(2)$ (spin) connection which is a covariant generalization of the self-dual Yang-Mills equations. Local…

We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on sigma-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show…

This work is divide in two cases. In the first case, we consider a spin manifold $M$ as the set of fixed points of an $S^{1}$-action on a spin manifold $X$, and in the second case we consider the spin manifold $M$ as the set of fixed points…

In part I, using the theory of $\infty$-categories, we constructed a natural ``continuous action'' of $\operatorname {Ham} (M, \omega) $ on the Fukaya category of a closed monotone symplectic manifold. Here we show that this action is…