Konferenz Asano - On lower bounds for the Kirby-Thompson nvarient by using homology groups

Abstract

A trisection is a decomposition of a 4-manifold into three 1-handlebodies. Kirby and Thompson introduced a non-negative integer-valued invariant of a closed 4- manifold by using trisections. This invariant is called the Kirby-Thompson invariant. In this talk, we give some lower bounds for the Kirby-Thompson invariant of certain 4-manifolds by using the 1st betti number and the 2nd homology group. As an application, we give a lower bound for the Kirby-Thompson invariant of Σg × Σh.

1. Einführung

Satz (Author)

Gilt $X≆X^{\prime }\#S^1\times S^3$, dann gilt eine Abschätzung der Kirby-Thompson-Invariante $L_X\ge 3b_1(X)$ Was ist $b_1$?

Satz Ogawa

Gilt $L_X\le 2$, dann ist $X$ eine Summe von $S^4,C{P}^2,S^1\times S^2,S^2\times S^2$

2. Review von Trisektionen

Siehe Trisektion (4D-Mannigfaltigkeit) und Trisektionsdiagramm.