Related papers: Higher \A-genera on certain non-spin $S^1$-manifol…

Let $M$ be an oriented even-dimensional Riemannian manifold on which a discrete group $\Gamma$ of orientation-preserving isometries acts freely, so that the quotient $X=M/\Gamma$ is compact. We prove a vanishing theorem for a half-kernel of…

We show in this short note that if a rational linear combination of Pontrjagin numbers vanishes on all simply-connected $4k$-dimensional closed connected and oriented spin manifolds admitting a Riemannian metric whose Ricci curvature is…

The main result of this note is that every closed Hamiltonian S^1 manifold is uniruled, i.e. it has a nonzero Gromov--Witten invariant one of whose constraints is a point. The proof uses the Seidel representation of \pi_1 of the Hamiltonian…

Motivated by string field theory, we explore various algebraic aspects of higher spin theory and Vasiliev equation in terms of homotopy algebras. We present a systematic study of unfolded formulation developed for the higher spin equation…

In this article we study the space of positive scalar curvature metrics on totally nonspin manifolds with spin boundary. We prove that for such manifolds of certain dimensions, those spaces are not connected and have nontrivial fundamental…

In this note, we generalize Gromov's reduction \cite{Gro20} from the aspherical conjecture to the generalized filling radius conjecture to the smooth $\mathbb Q$-homology vanishing conjecture for hypersurface. In particular, we can show…

Analysis of the first-order corrections to higher-spin equations is extended to homotopy operators involving shift parameters with respect to the spinor $Y$ variables, the argument of the higher-spin connection $\omega(Y)$ and the argument…

We show that every closed, simply connected, spin topological 4-manifold except $S^4$ and $S^2\times S^2$ admits a homologically trivial, pseudofree, locally linear action of $\mathbb{Z}_p$ for any sufficiently large prime number $p$ which…

An example of a higher spin gravity in four-dimensional flat space has recently been constructed in arXiv:1609.04655 [hep-th]. This theory is chiral and the action is written in the light-cone gauge. The theory has certain stringy features,…

We construct the effective field theory for a single massive higher-spin particle in flat spacetime. Positivity bounds of the S-matrix force the cutoff of the theory to be well below the naive strong-coupling scale, forbid any potential and…

Let $A$ be a unital simple separable exact C$^*$-algebra which is approximately divisible and of real rank zero. We prove that the set of positive elements in $A$ with a fixed non-compact Cuntz class has vanishing homotopy groups. Combined…

Let $M$ be a smooth, orientable, closed, connected $4$-manifold and suppose that $H_1(M;\mathbb{Z})$ is finitely generated and has no $2$-torsion. We give a homotopy decomposition of the suspension of $M$ in terms of spheres, Moore spaces…

We define and study the signature, A-hat genus and higher signatures of the quotient space of an $S^1$-action on a closed oriented manifold. We give applications to questions of positive scalar curvature and to an Equivariant Novikov…

We give a one-parameter family of exact solutions to four-dimensional higher-spin gauge theory invariant under a deformed higher-spin extension of SO(3,1) and parameterized by a zero-form invariant. All higher-spin gauge fields vanish,…

A combination of Bestvina--Brady Morse theory and an acyclic reflection group trick produces a torsion-free finitely presented Q-Poincar\'e duality group which is not the fundamental group of an aspherical closed ANR Q-homology manifold.…

We prove that if $X$ is a compact, oriented, connected $4$-dimensional smooth manifold, possibly with boundary, satisfying $\chi(X)\neq 0$, then there exists an integer $C\geq 1$ such that any finite group $G$ acting smoothly and…

We prove the vanishing of bounded cohomology with separable dual coefficients for many groups of interest in geometry, dynamics, and algebra. These include compactly supported structure-preserving diffeomorphism groups of certain manifolds;…

We present explicit formulas for the spectra of higher spin operators on the subbundle of the bundle of spinor-valued trace free symmetric tensors that are annihilated by the Clifford multiplication over the standard sphere in odd…

The geography and botany of smooth/symplectic nonspin 4-manifolds with abelian fundamental group are addressed.

We prove that for many degrees in a stable range the homotopy groups of the moduli space of metrics of positive scalar curvature on S^n and on other manifolds are non-trivial. This is achieved by further developing and then applying a…