Related papers: A Monster Tower Approach to Goursat Multi-Flags

Inspired by the Odlyzko root discriminant and Golod--Shafarevich $p$-group bounds, Martinet (1978) asked whether an imaginary quadratic number field $K/\mathbb{Q}$ must always have an infinite Hilbert $2$-class field tower when the class…

Building on work of Kapouleas and Yang, we construct sequences of minimal surfaces embedded in the round 3-sphere which converge to the Clifford torus counted with multiplicity two and have second fundamental form blowing up at every point…

Fock modules for multi-dimensional Virasoro algebras (non-central extensions of the diffeomorphism algebra vect(N)) have recently been reported. Using ideas from the antifield formalism, I construct new classes of lowest-energy modules, as…

If a finite group of orientation-preserving diffeomorphisms of the 3-dimensional torus leaves invariant an oriented, closed, embedded surface of genus g>1 and preserves the orientation of the surface, then its order is bounded from above by…

We provide an introduction to the concepts of holoraumy tensors, Lorentz covariant four-dimensional "Gadgets", and Gadget angles within the context of 4D N = 2 supermultiplets. This is followed by the calculation of the holoraumy tensors,…

The fixed point building of a polarity of a Moufang quadrangle of type $F_4$ is a Moufang set, as is the fixed point building of a semi-linear automorphism of order $2$ of a Moufang octagon that stabilizes at least two panels of one type…

The classical Poincar{\'e} conjecture that every homotopy 3-sphere is diffeomorphic to the 3-sphere is confirmed by Perelman in arXiv papers solving Thurston's program on geometrizations of 3-manifolds. A new confirmation of this conjecture…

The Witt ring of a complex flag variety describes the interesting -- i.e. torsion -- part of its topological KO-theory. We show that for a large class of flag varieties, these Witt rings are exterior algebras, and that the degrees of the…

Differential-geometric structures on the space of orbits of a finite Coxeter group, determined by Groth\'endieck residues, are calculated. This gives a construction of a 2D topological field theory for an arbitrary Coxeter group.

We discuss some categorical aspects of the objects that appear in the construction of the Monster and other sporadic simple groups. We define the basic representation of the categorical torus $\mathcal T$ classified by an even symmetric…

We prove several new results about the topology of fibers of Gelfand--Zeitlin systems on unitary and orthogonal coadjoint orbits, at the same time finding a unifying framework recovering and shedding light on essentially all known results.…

We show how to measure the failure of the Whitney trick in dimension 4 by constructing higher- order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on…

For a genus-1 1-bridge knot in the 3-sphere, that is, a (1,1)-knot, a middle tunnel is a tunnel that is not an upper or lower tunnel for some (1,1)-position. Most torus knots have a middle tunnel, and non-torus-knot examples were obtained…

We classify the epimorphisms of the buildings ${BC}_l(K,K_0,\sigma,L, q_0)$, where l is at least two, of pseudo-quadratic form type. This completes the classification of epimorphisms of irreducible spherical Moufang buildings of rank at…

In this article we continue the investigation of the length of the narrow $2$-class field tower of real quadratic number fields $\mathrm{k}$ whose discriminants are not a sum of two squares and for which their $2$-class groups are…

We give effective bounds for the class number of any algebraic function field of genus $g$ defined over a finite field. These bounds depend on the possibly partial information on the number of places on each degree $\leq g$. Such bounds are…

We characterize f-vectors of sufficiently large three-dimensional flag Gorenstein* complexes, essentially confirming a conjecture of Gal [Discrete Comput. Geom., 34 (2), 269--284, 2005]. In particular, this characterizes f-vectors of large…

We present a geometric approach to the Baum-Connes conjecture with coefficients for Gromov monster groups via a theorem of Khoskham and Skandalis. Secondly, we use recent results concerning the a-T-menability at infinity of large girth…

Let $G$ be the general linear group of the degree $n\geq 2$ over the field $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$. In this article, we give a description of orbit decomposition of the multiple projective space $G^m/P^m$ under the diagonal…

This note is devoted to studying certain families of elliptic surfaces with infinitely many fibers with rank at least 3 or 4 revisiting and combining ideas from of Gary Walsh, Salgado and Loughran, and the author.