arXiv subjects

Masayuki Yamasaki

Publications and source records attributed to Masayuki Yamasaki.

6 recordsLinked to original sources

arXiv2017

Whitney-type Formula for Non-null-homotopic Curves on Aspherical Surfaces

In an earlier paper, I defined a new winding number of regular closed curves on complete euclidean/hyperbolic surfaces and showed that this winding number, together with the free homotopy class, determines the regular homotopy class. In this paper, I give a Whitney-type formula for the winding number of non-null-homotopic generic regular closed curves on surfaces with a complete euclidean or hyperbolic structure, generalizing the formula for curves on a torus by Tanio and Kobayashi.

math.GT↗

arXiv2017

Winding numbers of regular closed curves on aspherical surfaces

We define winding numbers of regular closed curves on surfaces with a nice euclidean or hyperbolic geometry. We prove that two regular closed curves are regularly homotopic if and only if they are freely homotopic and have the same winding number.

math.GT↗

arXiv2009

Controlled L-theory

We develop an epsilon-controlled algebraic L-theory, extending our earlier work on epsilon-controlled algebraic K-theory. The controlled L-theory is very close to being a generalized homology theory; we study analogues of the homology exact sequence of a pair, excision properties, and the Mayer--Vietoris exact sequence. As an application we give a controlled L-theory proof of the classic theorem of Novikov on the topological invariance of the rational Pontrjagin classes.

math.GT↗

arXiv2009

Stability in controlled L-theory

We prove a squeezing/stability theorem for delta-epsilon controlled L-groups when the control map is a fibration on a finite polyhedron. A relation with boundedly-controlled L-groups is also discussed.

math.GT↗

arXiv2008

Local Indices of a Vector Field at an Isolated Zero on the Boundary

We define two types of local indices of a vector field at an isolated zero on the boundary, and prove Poincare-Hopf-type index theorems for certain vector fields on a compact smooth manifold which have only isolated zeros.

math.GT↗

arXiv2006

3-manifolds and 4-dimensional surgery

Let $X$ be a connected compact 3-manifold with non-empty boundary. Consider the boundary $M$ of $X\times D^2$. $M$ is a 4-dimensional closed manifold and has the same fundamental group as $X$. Various examples of $X$ are known for which a certain assembly map $A:H_4(X;L)\to L_4(π_1(X))$ is injective. For such an $X$ and any CW-spine $B$ of $X$, there is a $UV^1$-map $p:M\to B$. For any $ε>0$, if the surgery obstruction for a TOP normal map $(f,b):N\to M$ vanishes, we can perform surgery on $f$ to change it into a $p^{-1}(ε)$-controlled homotopy equivalence.

math.GT↗