arXiv subjects

Yoshihiro Fukumoto

Publications and source records attributed to Yoshihiro Fukumoto.

4 recordsLinked to original sources

arXiv2026

Real Floer Homotopy Types and $w$-Invariants

We express the local-equivalence classes of real Seiberg--Witten Floer homotopy types for spin Seifert $3$-manifolds with certain odd involutions in terms of the Fukumoto-Furuta $w$-invariant. The proof uses real orbifold Bauer-Furuta invariant for a class of spin $4$-orbifolds constructed by Fukumoto-Furuta-Ue. For torus knots, we prove that the local-equivalence classes of real Floer homotopy types associated with their $2^k$-fold cyclic branched covers are eventually periodic in $k$. Finally, we prove that the integer-valued concordance homomorphisms $\{8δ_R^{(k)}\}_{k\geq1}$ are linearly independent.

math.GT↗

arXiv2025

On the connected sums of the $(2,1)$-cable of the figure eight knot

We show that the 3-fold (resp. 6-fold) connected sum of the $(2,1)$-cable of the figure-eight knot cannot bound a smooth null-homologous disk in a punctured $S^2 \times S^2$ (resp. in a punctured $#_2 S^2 \times S^2$. This result is obtained using a real version of the $10/8$-inequality established by Konno, Miyazawa, and Taniguchi.

math.GT↗

arXiv2013

Traceless SU(2) representations of 2-stranded tangles

Given a 2-stranded tangle in a $\ZZ/2$ homology ball, $T\subset Y$, we investigate the character variety $R(Y,T)$ of conjugacy classes of traceless SU(2) representations of $π_1(Y\setminus T)$. In particular we completely determine the subspace of binary dihedral representations, and identify all of $R(Y,T)$ for many tangles naturally associated to knots in S^3. Moreover, we determine the image of the restriction map from $R(T,Y)$ to the traceless SU(2) character variety of the 4-punctured 2-sphere (the {\it pillowcase}). We give examples to show this image can be non-linear in general, and show it is linear for tangles associated to pretzel knots.

math.GT↗

arXiv2009

Cobordism category of plumbed 3-manifolds and intersection product structures

In this paper, we introduce a category of graded commutative rings with certain algebraic morphisms, to investigate the cobordism category of plumbed 3-manifolds. In particular, we define a non-associative distributive algebra that gives necessary conditions for an abstract morphism between the homologies of two plumbed 3-manifolds to be realized geometrically by a cobordism. Here we also consider the homology cobordism monoid, and give a necessary condition using w-invariants for the homology 3-spheres to belong to the inertia group associated to some homology 3-spheres.

math.GT↗