Related papers: Commensurations of the Johnson kernel

We investigate oriented graphs based on the curve complex $C(S)$ of a closed surface $S$ and induced by functions on the vertex set of $C(S)$. In particular, we introduce the Dehn quasi-homothetic functions, which behave similarly to…

We provide some language for algebraic study of the mapping class groups for surfaces with non-connected boundary. As applications, we generalize our previous results on Dehn twists to any compact connected oriented surfaces with non-empty…

Let K be the kernel of an epimorphism G -> Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3, or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group…

Cobordism groups of cooriented fold maps of codimension 1 are computed completely. Namely their odd torsion part coincides with that of the stable homotopy group of spheres in the same dimension, while the 2-primary part is the kernel of…

Let A be the mod 2 Steenrod algebra, and let Q denote the category of exterior sub-Hopf algebras of A, where the morphisms are given by inclusions. The restriction maps Ext_A (Z/2,Z/2) --> Ext_E (Z/2,Z/2), for E in Q, can be assembled into…

We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is naturally isomorphic to the second lazy cohomology group of…

We study the quotient of the mapping class group $\operatorname{Mod}_g^n$ of a surface of genus $g$ with $n$ punctures, by the subgroup $\operatorname{Mod}_g^n[p]$ generated by the $p$-th powers of Dehn twists. Our first main result is that…

This note is the sequel to [A note on secondary K-theory. Algebra and Number Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of noncommutative motives, we prove that the canonical map from the derived Brauer group to the…

We show that every involutive Hopf monoid in a complete and finitely cocomplete symmetric monoidal category gives rise to invariants of oriented surfaces defined in terms of ribbon graphs. For every ribbon graph this yields an object in the…

Let K be a global function field of positive characteristic p and let M be a (commutative) finite and flat K-group scheme. We show that the kernel of the canonical localization map H^{1}(K,M)\to\prod_{all v}H^{1}(K_{v},M) in flat (fppf)…

The fine curve graph of a surface was introduced by Bowden, Hensel, and Webb as a graph consisting of essential simple closed curves on the surface. Long, Margalit, Pham, Verberne, and Yao proved that the automorphism group of the fine…

Klein's simple group $H$ of order $168$ is the automorphism group of the plane quartic curve $C$, called Klein quartic. By Torelli Theorem, the full automorphism group $G$ of the Jacobian $J=J(C)$ is the group of order $336$, obtained by…

Let $X/S$ be a smooth family of smooth projective varieties, where $S$ is a smooth affine curve over a field $k$ of characteristic $0.$ We relate the differential fundamental groupoid scheme of $X/k$ with the differential fundamental…

Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\lambda$ be a simplicial map of the complex of curves, $\mathcal{C}(N)$, on $N$ which satisfies the following: $[a]$ and $[b]$ are…

We study the topology of spaces related to Kac-Moody groups. Given a split Kac-Moody group over the complex numbers, let K denote the unitary form with maximal torus T having normalizer N(T). In this article we study the cohomology of the…

We study Hopf algebras via tools from geometric invariant theory. We show that all the invariants we get can be constructed using the integrals of the Hopf algebra and its dual together with the multiplication and the comultiplication, and…

Lov\'{a}sz proved that two graphs $G$ and $H$ are isomorphic if $\hom(K,G) = \hom(K,H)$ for all graphs $K$, where $\hom(G_1,G_2)$ denotes the number of homomorphisms from $G_1$ to $G_2$. Dvo\v{r}\'{a}k showed that it suffices to count…

We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map, denoted by $e$, from the $0$-connective algebraic $K$-theory space of the complex…

Let $G$ and $H$ be locally compact groups and consider their associate spaces of almost periodic functions $AP(G)$ and $AP(H)$. We investigate the continuous group homomorphisms induced by isometries of $AP(G)$ into $AP(H)$. Among others,…

For any odd prime $p$, we prove that the induced homomorphism from the mod $p$ cohomology of the classifying space of a compact simply-connected simple connected Lie group to the Weyl group invariants of the mod $p$ cohomology of the…