Related papers: The 2-primary Hurewicz image of tmf
We construct large families of harmonic morphisms which are holomorphic with respect to Hermitian structures by finding heierarchies of Weierstrass-type representations. This enables us to find new examples of complex-valued harmonic…
This paper is on the Curtis conjecture. We show that the image of the Hurewicz homomorhism $h:\pi_*Q_0S^0\to H_*(Q_0S^0;\mathbb{Z})$, when restricted to product of positive dimensional elements, is determined by…
We compute the mod 2 homology of spin mapping class groups in the stable range. In earlier work we computed the stable mod p homology of the oriented mapping class group, and the methods and results here are very similar. The forgetful map…
We implement the geometric method proposed in ([9], [3], [16]) to analytically predict the sequence of bifurcations leading to a change of stability and/or the appearance of new periodic orbits in the secular 3D planetary three body…
This paper is a step towards the complete topological classification of {\Omega}-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and sufficient conditions for two such diffeomorphisms to be topologically…
In this article we study persistence features of topological entropy and periodic orbit growth of Hamiltonian diffeomorphisms on surfaces with respect to Hofer's metric. We exhibit stability of these dynamical quantities in a rather strong…
We study the stable motivic homotopy groups $\pi_{s,w}$ of the 2-completion of the motivic sphere spectrum over $\mathbb{C}$. When arranged in the $(s,w)$-plane, these groups break into four different regions: a vanishing region, an…
Let $F\in\mathrm{Diff}(\mathbb{C}^2,0)$ be a germ of a holomorphic diffeomorphism and let $\Gamma$ be an invariant formal curve of $F$. Assume that the restricted diffeomorphism $F|_{\Gamma}$ is either hyperbolic attracting or rationally…
The Kowalevski gyrostat in two constant fields is known as the unique example of an integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions and still having the clear mechanical…
Generalizing homogeneous spectra for rings graded by natural numbers, we introduce multihomogeneous spectra for rings graded by abelian groups. Such homogeneous spectra have the same completeness properties as their classical counterparts,…
Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E_infinity-ring spectrum, based on the study of elliptic curves with level-3 structure. We show that the natural map…
We characterize the Hurewicz cofibrations between finite topological spaces, that is, the continuous functions between finite topological spaces that have the homotopy extension property with respect to all topological spaces. In…
The eigenfamilies of Gudmundsson and Sakovich can be used to generate harmonic morphisms, proper $r$-harmonic maps, and minimal co-dimension $2$ submanifolds. This article begins by characterising the globally defined eigenfamilies of the…
For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and…
We compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving questions about convergence and differentials in the slice…
We consider general fermionic quantum field theories with a global finite group symmetry $G$, focusing on the case of 2-dimensions and torus spacetime. The modular transformation properties of the family of partition functions with…
We show the problem of counting homomorphisms from the fundamental group of a homology $3$-sphere $M$ to a finite, non-abelian simple group $G$ is #P-complete, in the case that $G$ is fixed and $M$ is the computational input. Similarly,…
We study the statistics of Hamiltonian cycles on various families of bicolored random planar maps (with the spherical topology). These families fall into two groups corresponding to two distinct universality classes with respective central…
We show that $v_2^9$ is a permanent cycle in the 3-primary Adams-Novikov spectral sequence computing $\pi_*(S/(3,v_1^8))$, and use this to conclude that the families $\beta_{9t+3/i}$ for $i=1,2$, $\beta_{9t+6/i}$ for $i=1,2,3$,…
In this paper we first prove a characterization formula for biharmonic maps in Euclidean spheres and, as an application, we construct a family of biharmonic maps from a flat $2$-dimensional torus $\mathbb{T}$ into the $3$-dimensional unit…