Related papers: The Equivariant Slice Filtration: a Primer
A geometric argument is given to prove that the Seifert genus of a positive knot equals its slice genus. A combinatorial invariant, giving a lower bound for the slice genus, is formulated for arbitrary knots. Properties and applications of…
Two parameter families of plane conics are called nets of conics. There is a natural group action on the vector space of nets of conics, namely the product of the group reparametrizing the underlying plane, and the group reparametrizing the…
This paper describes the relationship between the first non-vanishing Milnor invariants of a classical link and the intersection invariant of a twisted Whitney tower. This is a certain 2-complex in the 4-ball, built from immersed disks…
We can construct a 4-manifold by attaching 2-handles to a 4-ball with framing r along the components of a link in the boundary of the 4-ball. We define a link as r-shake slice if there exists embedded spheres that represent the generators…
A classic result of Anderson, Brown, and Peterson states that the cobordism spectrum MSpin (respectively, MSpin$^c$) splits as a sum of Eilenberg--Mac Lane spectra and connective covers of real K-theory (respectively, complex K-theory) at…
In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quaternionic Fock and Bergman spaces in this new setting. In…
We consider divisorial filtration on the rings of functions on hypersurface singularities associated with Newton diagrams and their analogues for plane curve singularities. We compute the multi-variable Poincar\'e series for the latter…
Let $\pi$ be a group equipped with an action of a second group $G$ by automorphisms. We define the equivariant cohomological dimension ${\sf cd}_G(\pi)$, the equivariant geometric dimension ${\sf gd}_G(\pi)$, and the equivariant…
Toric ideals to hierarchical models are invariant under the action of a product of symmetric groups. Taking the number of factors, say m, into account, we introduce and study invariant filtrations and their equivariant Hilbert series. We…
Inspired from the Cholewinski approach see [5], we investigate a family of Fock spaces in the quaternionic slice hyperholomorphic setting as well as some associated quaternionic linear operators. In a particular case, we reobtain the slice…
These notes were prepared to accompany a sequence of three lectures at the conference Winterbraids XI in Dijon, held in December 2021. In them, we provide an introduction to slice knots and the equivalence relation of concordance. We…
We provide a structural analysis for McCarthy algebras, the variety generated by the three-element algebra defining the logic of McCarthy (the non-commutative version of Kleene three-valued logics). Our analysis will be conducted in a very…
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and…
Starting from the data of a nonsingular complex projective toric variety, we define an associated notion of toric co-Higgs bundle. We provide a Lie-theoretic classification of these objects by studying the interaction between Klyachko's fan…
We generalize the representation formula from slice-domains of regularity to general Riemann slice-domains. This result allows us to extend the $*$-product of slice regular functions on axially symmetric domains to certain Riemann…
We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged…
Every $(\infty, n)$-category can be approximated by its tower of homotopy $(m, n)$-categories. In this paper, we prove that the successive stages of this tower are classified by k-invariants, analogously to the classical Postnikov tower for…
In this paper, we initiate the study of the geometric function theory for slice starlike functions over quaternions and its subclasses. This allows us to answer negatively some questions about the Bieberbach conjecture, the growth,…
Orthogonal projections of the uniform measure on the Sierpinski triangle form a family of self similar measures with overlaps. The main result of this work is to make a connection between the dimension theory of these measures and the…
We use Lee's work on the Khovanov homology to define a knot invariant s. We show that s(K) is a concordance invariant and that it provides a lower bound for the slice genus of K. As a corollary, we give a purely combinatorial proof of the…