On the history of the Hopf problem

Ilka Agricola; Giovanni Bazzoni; Oliver Goertsches; Panagiotis Konstantis; Sönke Rollenske

doi:10.1016/j.difgeo.2017.10.014

Home/Archive/arXiv

arXiv · 1708.01068

On the history of the Hopf problem

Ilka Agricola·Giovanni Bazzoni·Oliver Goertsches·Panagiotis Konstantis·Sönke Rollenske

View original source ↗Read source document ↗Export metadata ↓

Abstract

This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on $S^6$?" This unsolved mathematical question was the subject of the Conference "MAM 1 $-$ (Non-)Existence of Complex Structures on $S^6$", which took place at Philipps-Universität Marburg, Germany, between March 27th and March 30th, 2017.

Explore related subjects

math.HO math.AG math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ilka Agricola, Giovanni Bazzoni, Oliver Goertsches, Panagiotis Konstantis, Sönke Rollenske. 2017-08-03. On the history of the Hopf problem. https://doi.org/10.1016/j.difgeo.2017.10.014

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Come for the vibe, stay for the math

This article describes our experiences in mathematical outreach over the past decade. We talk about specific activities, but also general principles that we've learned along the way.

math.HO↗

arXiv2026

Notes on a strongly aperiodic monotile in $E^3$

We provide a clearer presentation of the Chair44 monotile, a new strongly aperiodic monotile in three-dimensional Euclidean space $E^3$.

math.HO↗

arXiv2026

From foundations to applications: reverse mathematics and philosophy

Reverse mathematics is a branch of mathematical logic dedicated to determining the minimal set existence principles necessary and sufficient to derive ordinary mathematical theorems about concrete structures like the real line. Since the mid-1970s, reverse mathematics has developed a systematic classification of the strength of theorems in areas of mathematics ranging from real and complex analysis to infinitary combinatorics. This essay will place reverse mathematics in its historical and philosophical context, and reveal its relevance to central issues in the philosophy of mathematics, from the foundational programmes of Hilbert and Brouwer to contemporary debates about realism, determinacy, and applicability of mathematics. In doing so, it will discuss the role of computability theory in measuring the strength of set existence principles, as well as related questions about idealisation when these principles are applied in the physical sciences and in philosophy.

math.HO↗