Related papers: Line Bundle Twists for Unitary Bordism are Ghosts

An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which…

We show that in the decoupling limit of an F-theory compactification, the internal directions of the seven-branes must wrap a non-commutative four-cycle S. We introduce a general method for obtaining fuzzy geometric spaces via toric…

We show that the nefness of the canonical bundle of compact K\"ahler threefolds is invariant under deformed symplectic diffeomorphisms.

Let S be an essentially smooth scheme over a field of characteristic exponent c. Let MGL and HZ denote the algebraic cobordism spectrum and the motivic cohomology spectrum over S, respectively. We show that the canonical map MGL/(a1, a2,…

This paper is our first step in establishing a de Rham model for equivariant twisted $K$-theory using machinery from noncommutative geometry. Let $G$ be a compact Lie group, $M$ a compact manifold on which $G$ acts smoothly. For any $\alpha…

We study corners and fundamental corners of the irreducible representations of the groups G=Spin(n,1) that are not elementary, i.e. that are equivalent to subquotients of reducible nonunitary principal series representations. For even n we…

In this paper, we show that the Gluck twist of certain satellite $2$-knots in a $4$-manifold do not change the diffeomorphism type in three different ways: one is directly from the definition of the satellite $2$-knot, and the other two are…

We prove that if $X$ is a complex projective K3 surface and $g>0$, then there exist infinitely many families of curves of geometric genus $g$ on $X$ with maximal, i.e., $g$-dimensional, variation in moduli. In particular every K3 surface…

Let $\Gamma$ be a discrete countable group acting isometrically on a measurable field $\mathbf{X}$ of CAT(0)-spaces of finite telescopic dimension over some ergodic standard Borel probability $\Gamma$-space $(\Omega,\mu)$. If $\mathbf{X}$…

A theorem by Mumford implies that every automorphic line bundle on a pure open Shimura variety, equipped with an invariant smooth metric, can be uniquely extended as a line bundle on a toroidal compactification of the variety, in such a way…

Solitonic symmetry has been believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover…

In this paper, we introduce a bordism category $\mathcal{C}_d^{PL}$ whose objects are bundles of closed $(d-1)$-dimensional piecewise linear manifolds and whose morphisms are bundles of $d$-dimensional piecewise linear cobordisms. In the…

We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct the associated analytic torsion form T. If Z is a smooth closed aspherical manifold, we show that T gives…

A $\mathbb Q$-conic bundle germ is a proper morphism from a threefold with only terminal singularities to the germ $(Z \ni o)$ of a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We obtain…

We prove that any minimal weak symplectic filling of the canonical contact structure on the unit cotangent bundle of a nonorientable closed surface other than the real projective plane is s-cobordant rel boundary to the disk cotangent…

We study the $H^3$ invariant of a group homomorphism $\phi:G \rightarrow \mathrm{Out}(A)$, where $A$ is a classifiable C$^*$-algebra. We show the existence of an obstruction to possible $H^3$ invariants arising from considering the unitary…

We prove that every toric quiver flag variety $Y$ is isomorphic to a fine moduli space of cyclic modules over the algebra $\text{End}(T)$ for some tilting bundle $T$ on $Y$. This generalises the well known fact that $\mathbb{P}^n$ can be…

We analyze Yukawa unification in the the context of $E_8\times E_8$ heterotic Calabi-Yau models which rely on breaking to a GUT theory via a non-flat gauge bundle and subsequent Wilson line breaking to the standard model. Our focus is on…

Over any field of characteristic $0$, we prove that the homotopy exact sequence of algebraic fundamental groups for the universal curve with unordered marked points does not split. The same nonsplitting holds for the universal hyperelliptic…

In a recent paper, the authors proved that no spin foliation on a compact enlargeable manifold with Hausdorff homotopy graph admits a metric of positive scalar curvature on its leaves. This result extends groundbreaking results of…