(Z2)k-actions with disconnected fixed point set☆☆This work is supported by the Japanese Government Scholarship.

Fixed Point Formulas and Loop Group Actions

In this paper we present a new fixed point formula associated with loop group actions on infinite dimensional manifolds. This formula provides information for certain infinite dimensional situations similarly as the well known Atiyah-BottSegal-Singer’s formula does in finite dimension. A generalization of the latter to orbifolds will be used as an intermediate step. There exist extensive litera...

The Rational Homotopy of Fixed Point Sets of Torus Actions

A Point Set Whose Space of Triangulations Is Disconnected

In this paper we explicitly construct a triangulation of a 6-dimensional point configuration of 324 points which admits no geometric bistellar operations (or flips, for short). This triangulation is an isolated element in the graph of triangulations of the point configuration. It has been a central open question in polytope combinatorics in the last decade whether point configurations exist for...

Characteristic Fixed-Point Sets of Semifree Actions on Spheres

A group action is semifree if it is free away from its fixed-point set. P. A. Smith showed that when a finite group of order q acts semifreely on a sphere, the fixed set is a mod q homology sphere. Conversely, given a mod q homology sphere as a subset of a sphere, one may try to construct a group action on the sphere fixing the subset. The converse question was first systematically studied by J...

Fixed-Point Free Circle Actions on 4-Manifolds

This paper is concerned with fixed-point free S-actions (smooth or locally linear) on orientable 4-manifolds. We show that the fundamental group plays a predominant role in the equivariant classification of such 4-manifolds. In particular, it is shown that for any finitely presented group with infinite center, there are at most finitely many distinct smooth (resp. topological) 4-manifolds which...