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Topological line arrangements and their topological invariants
Sakumi Sugawara
A topological line arrangement is an arrangement of embedded spheres in the complex projective plane that topologically generalizes a complex line arrangement. In this paper, we es…
The cohomology ring of the boundary manifold of a combinatorial line arrangement
Sakumi Sugawara
We compute the integral cohomology rings of the associated -manifold called the \textit{boundary manifold} for a combinatorial line arrangement, and prove that it is isomorphic…
First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in
Sakumi Sugawara
We study the Milnor fiber boundary for hyperplane arrangements in . This is one of the examples of non-isolated surface singularities, which are studied by Némethi--S…
Homogeneous quandles with abelian inner automorphism groups
Takuya Saito, Sakumi Sugawara
In this paper, we give a characterization of homogeneous quandles with abelian inner automorphism groups. In particular, we show that such a quandle is expressed as an abelian exte…
Divides with cusps and symmetric links
Sakumi Sugawara
A Divide with cusps is the image of a proper generic immersion from finite intervals and circles into a -disk which allows to have cusps. A divide with cusps is the generalizati…
Handle decompositions and Kirby diagrams for the complement of plane algebraic curves
Sakumi Sugawara
The complement of plane algebraic curves are well studied from topological and algebro-geometric viewpoints. In this paper, we will describe the explicit handle decompositions and…
-local system cohomology of hyperplane arrangements and a Cohen-Dimca-Orlik type theorem
Sakumi Sugawara
Local system cohomology groups of the complements of hyperplane arrangements have played an important role in the theory of hypergeometric integrals, the topology of Milnor fibers…
Betti numbers and torsions in homology groups of double coverings
Suguru Ishibashi, Sakumi Sugawara, Masahiko Yoshinaga
Papadima and Suciu proved an inequality between the ranks of the cohomology groups of the Aomoto complex with finite field coefficients and the twisted cohomology groups, and conje…
Divides with cusps and Kirby diagrams for line arrangements
Sakumi Sugawara, Masahiko Yoshinaga
The complement of a complexified real line arrangement is an affine surface. It is classically known that such a space has a handle decomposition up to -handles. We will describ…