Related papers: A combinatorial invariant for Spherical CR structu…

Some aspects of the construction of SW Floer homology for manifolds with non-trivial rational homology are analyzed. In particular, the case of manifolds that are obtained as zero-surgery on a knot in a homology sphere, and for torsion…

Invariants for framed links in $S^3$ obtained from Chern-Simons gauge field theory based on an arbitrary gauge group (semi-simple) have been used to construct a three-manifold invariant. This is a generalization of a similar construction…

In a previous paper we have constructed an invariant of four-dimensional manifolds with boundary in the form of an element in the stable homotopy group of the Seiberg-Witten Floer spectrum of the boundary. Here we prove that when one glues…

The main result of this paper is that the identity component of the automorphism group of a compact, connected, strictly pseudoconvex CR manifold is compact unless the manifold is CR equivalent to the standard sphere. In dimensions greater…

We determine the local equivalence class of the Seiberg-Witten Floer stable homotopy type of a spin rational homology 3-sphere $Y$ embedded into a spin rational homology $S^{1} \times S^{3}$ with a positive scalar curvature metric so that…

We construct CR mappings between spheres that are invariant under actions of finite unitary groups. In particular, we combine a tensoring procedure with D'Angelo's construction of a canonical group-invariant CR mapping to obtain new…

We define an invariant $\nabla_G(M)$ of pairs M,G, where M is a 3-manifold obtained by surgery on some framed link in the cylinder $S\times I$, S is a connected surface with at least one boundary component, and G is a fatgraph spine of S.…

Let $\langle I_{1}, I_{2}, I_{3}\rangle$ be the complex hyperbolic $(4,4,\infty)$ triangle group. In this paper we give a proof of a conjecture of Schwartz for $\langle I_{1}, I_{2}, I_{3}\rangle$. That is $\langle I_{1}, I_{2},…

E. Cartan's method of moving frames is applied to 3-dimensional manifolds $M$ which are CR-embedded in 5-dimensional real hyperquadrics $Q$ in order to classify $M$ up to CR symmetries of $Q$ given by the action of one of the Lie groups…

We construct a quartic threefold with L-rational singularities which has torsion in its middle homology group. This answers a question of Brown and Schnetz for all fields of characteristic zero.

A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and…

We introduce a fourth order CR invariant operator on pluriharmonic functions on a three-dimensional CR manifold, generalizing to the abstract setting the operator discovered by Branson, Fontana and Morpurgo. For a distinguished class of…

We introduce (co)homology theory for multiple group racks and construct cocycle invariants of compact oriented surfaces in the 3-sphere using their 2-cocycles, where a multiple group rack is a rack consisting of a disjoint union of groups.…

We establish a structural understanding of the involutive Heegaard Floer homology for all linear combinations of almost-rational (AR) plumbed three-manifolds. We use this to show that the Neumann-Siebenmann invariant is a homology cobordism…

Screw rotations in nonsymmorphic space group symmetries induce the presence of hourglass and accordion shape band structures along screw invariant lines whenever spin-orbit coupling is nonnegligible. These structures induce topological…

The purpose of this paper is to describe certain CR-covariant differential operators on a strictly pseudoconvex CR manifold $M$ as residues of the scattering operator for the Laplacian on an ambient complex K\"{a}hler manifold $X$ having…

We prove that, if M is a compact oriented manifold of dimension 4k+3, where k>0, such that pi_1(M) is not torsion-free, then there are infinitely many manifolds that are homotopic equivalent to M but not homeomorphic to it. To show the…

Let $G$ be a nonabelian, simple group with a nontrivial conjugacy class $C \subseteq G$. Let $K$ be a diagram of an oriented knot in $S^3$, thought of as computational input. We show that for each such $G$ and $C$, the problem of counting…

J.H.C. Whitehead introduced the concept of crossed modules in the early 20th century. These crossed modules are crucial for algebraic models of 2-type homotopy, which involve connected spaces with no higher than second-degree homotopy…

We prove that if $M$ is a CW-complex and $*$ is a 0-cell of $M$, then the crossed module $\Pi_2(M,M^1,*)$ does not depend on the cellular decomposition of $M$ up to free products with $\Pi_2(D^2,S^1,*)$, where $M^1$ is the 1-skeleton of…