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On two quotients of $S^2\times S^2$

Andrea Bianchi

Abstract

In this note we prove that two seemingly different smooth 4-manifolds arising as quotients of $S^2\times S^2$ by free actions of $\mathbb{Z}/4$ are in fact diffeomorphic, answering a question of Hambleton and Hillman.

On two quotients of $S^2\times S^2$

Abstract

In this note we prove that two seemingly different smooth 4-manifolds arising as quotients of by free actions of are in fact diffeomorphic, answering a question of Hambleton and Hillman.
Paper Structure (4 sections, 2 theorems)

This paper contains 4 sections, 2 theorems.

Table of Contents

  1. Introduction
  2. An alternative model for the two manifolds
  3. A family of actions
  4. Acknowledgments

Key Result

Theorem 1.1

The manifolds $M_1$ and $M_5$ are diffeomorphic.

Theorems & Definitions (5)

  • Theorem 1.1
  • Definition 2.1
  • Proposition 2.2
  • Definition 2.3
  • Definition 2.4