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The solution on the geography-problem of non-formal compact (almost) contact manifolds

Christoph Bock

Abstract

Let $(m,b)$ be a pair of natural numbers. For $m$ odd with $m \ge 7$ (resp. $m \ge 5$) and $b=1$ (resp. $b=0$) we show that there is a non-formal compact (almost) contact $m$-manifold with first Betti number $b_1 = b$. Moreover, in the case $b = 0$ with $m \ge 7$, the manifold even is simply-connected.

The solution on the geography-problem of non-formal compact (almost) contact manifolds

Abstract

Let be a pair of natural numbers. For odd with (resp. ) and (resp. ) we show that there is a non-formal compact (almost) contact -manifold with first Betti number . Moreover, in the case with , the manifold even is simply-connected.

Paper Structure

This paper contains 5 sections, 12 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Some five-dimensional contact solvmanifolds and the proof of Theorem \ref{['NewMain3']}
  3. Massey products
  4. Proof of Theorem \ref{['NewMain1']}
  5. Another proof of Theorem \ref{['NewMain2']} in the case $m \ge 13$

Key Result

Theorem 1.1

$\,$ Given $m \in \mathbb{N}_+$ and $b \in \mathbb{N}$, there are oriented compact $m$-dimensional manifolds with $b_1 = b$ which are non-formal if and only if one of the following conditions holds:

Theorems & Definitions (15)

  • Theorem 1.1: FMGeo
  • Theorem 1.2: ipse1
  • Theorem 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Remark
  • Proposition 1.6
  • Proposition 2.1
  • Theorem 2.2
  • Remark
  • ...and 5 more