Related papers: Generalized Dehn twists in low-dimensional topolog…

Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local…

Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the…

In this thesis we give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. In his seminal book, Connes constructs a map from the equivariant cohomology of a manifold carrying the…

In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion…

By using a notion of a geometric Dehn twist in $\sharp_k(S^2 \times S^1)$, we prove that when projections of two $\mathbb{Z}$-splittings to the free factor complex are far enough from each other in the free factor complex, Dehn twist…

Non-trivial examples of generalized paracomplex structures (in the sense of the generalized geometry \`a la Hitchin) are constructed applying the twistor space construction scheme.

We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and a lower bound of numbers of generators for the twist…

We generalize the definition of thin position of Scharlemann and Thompson for compact orientable 3-manifolds with torus boundary components and introduce $\alpha$-sloped generalized Heegaard splittings. We examine its relationship to…

This is a PhD thesis in low-dimensional topology. Its main purpose is to examine so-called t\^ete-\`a-t\^ete twists. Those were defined by A'Campo and give an easy combinatorial description of certain mapping classes on surfaces with…

We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…

This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity: it has positive topological…

A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…

In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence…

Let $G$ be a group. The directed endomorphism graph, $\dend(G)$ of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex $a$ to the vertex $b$ if $a \neq b$ and there exists an endomorphism on $G$ mapping…

We classify homomorphisms from the braid group on $n$ strands to the pure mapping class group of a nonoriantable surface of genus $g$. For $n\ge 14$ and $g\le 2\lfloor{n/2}\rfloor+1$ every such homomorphism is either cyclic, or it maps…

We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…

This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…

We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…

We consider the universal family $E_n^d$ of superelliptic curves: each curve $\Sigma_n^d$ in the family is a $d$-fold covering of the unit disk, totally ramified over a set $P$ of $n$ distinct points; $\Sigma_n^d\hookrightarrow E_n^d\to…

We construct several families of embeddings of braid groups into mapping class groups of orientable and non-orientable surfaces and prove that they induce the trivial map in stable homology in the orientable case, but not so in the…