Compact Simply-connected Manifolds Research Articles

A-foliations of codimension two on compact simply-connected manifolds

We show that a singular Riemannian foliation of codimension two on a compact simply-connected Riemannian (n+2)-manifold, with regular leaves homeomorphic to the n-torus, is given by a smooth effective n-torus action. This solves in the negative for the codimension 2 case a question about the existence of foliations by exotic tori on simply-connected manifolds.

Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds

Let ƒ be a self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3, r a fixed natural number. In this paper we define a topological invariant which is the best lower bound for the number of r-periodic points for all C1 maps homotopic to ƒ. In case m = 3 we give the formula for and calculate it for self-maps of S2 × I.

Moduli space actions on the Hochschild co-chains of a Frobenius algebra I: cell operads

This is the first of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co-chains of a Frobenius algebra. We also prove that a there is dg-PROP action of a version of Sullivan chord diagrams which acts on the normalized Hochschild co-chains of a Frobenius algebra. These actions lift to operadic correlation functions on the co-cycles. In particular, the PROP action gives an action on the homology of a loop space of a compact simply-connected manifold. In this first part, we set up the topological operads/PROPs and their cell models. The main theorems of this part are: There is a cell model operad for the moduli space of genusg curves with n punctures and a tangent vector at each of these punctures, there exists a CW complex whose chains are isomorphic to a certain type of Sullivan chord diagrams and they form a PROP. Furthermore there exist weak versions of these structures on the topological level which all lie inside an all encompassing cyclic (rational) operad.

A hypercomplex stiefel manifold

We construct a hypercomplex structure on a compact simply-connected manifold derived from the hyperkähler structure of flat space.

Morse theory for codimension-one foliations

It is shown that a smooth codimension-one foliation on a compact simply-connected manifold has a compact leaf if and only if every smooth real-valued function on the manifold has a cusp singularity.

On the Minimal Ordered Morse Functions on Compact Simply-Connected Manifolds

Throughout this paper, (W ; V, V) denotes a compact smooth manifold triad of dimension n in the sense that dW=V(jV and VftV' = , and & the space of C°°-functions of (W; V, V) into (I; 0, 1) without critical points on the boundary. The codimension 0 stratum J^° of the natural stratification of J^ is the space of excellent functions ( = Morse functions with distinct critical values). By definition, jfej^ is called to be ordered and minimal, if the critical values are ordered in the order of their indices and the number of critical points is minimal with respect to the homology group structure of H#(W, V). Let / be an excellent function with m critical values v19. .., vm and put u0=v1/2, um — and u{ = (vt+vi+1)/2 for l^i^m — l. Then, (W, V) has a filtration Wf=(W»...9 WJ defined by W^f-^Q, w,] so that Wm = Wand Wf has a presentation of the handle-attaching form (Wf-!, f~(ui_-^ ; W such that (goh) | W,: Wt->Wf and (hog) IW,: W^W; are homotopy equivalences for every /.