Cyclic group actions on manifolds from deformations of rational homotopy types

Circle Actions on Rational Homology Manifolds and Deformations of Rational Homotopy Types

The aim of this paper is to follow up the program set in [LR85, Rau92], i.e., to show the existence of nontrivial group actions ("symmetries") on certain classes of manifolds. More specifically, given a manifold X with submanifold F , I would like to construct nontrivial actions of cyclic groups on X with F as fixed point set. Of course, this is not always possible, and a list of necessary cond...

Free Finite Group Actions on S by Ronnie Lee and Charles Thomas

In this paper we describe the first stages of a theory of 3-manifolds with finite fundamental group. The strong conjecture that any free finite group action on S is conjugate to a linear action is known for some cyclic groups, see [3], [4], and is supported by recent work of one of us on fundamental groups [2]. Here we concern ourselves with the weaker conjecture that any compact 3-manifold wit...

Symmetries on Manifolds, Deformations and Rational Homotopy: a Survey

Rational Homotopy Types of Mirror Manifolds

We explain how to relate the problem of finding a mirror manifold for a Calabi-Yau manifold to the problem of characterizing the rational homotopy types of closed Kähler manifolds. In this paper, we show that under a rationality condition on the (classical) Yukawa coupling constants for a Calabi-Yau manifold M , a rational homotopy type can be determined. If M has a mirror manifold M̃ , then M̃ h...

Isovariant mappings of degree 1 and the Gap Hypothesis

Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions—isovariant and equivariant— often coincide under a condition called the Gap Hypothesis; the proofs use deep results in geometric topology. This paper analyzes the difference between the two types of maps from a homotopy theoretic viewpoint more generally for degre...