Hi, All:(adsbygoogle = window.adsbygoogle || []).push({});

I hope I am not missing something obvious: can't we use the Jordan Curve Thm. to show

that the homology H_n(R^n) of R^n is trivial ? How about showing that Pi_n(R^n) is trivial?

It seems like the def. of cycles in a space X is geenralized by continuous , injective maps f: S^n -->X . When X=R^n, JCT says that f(S^n) separates R^n into 2 regions, which can be seen as saying that f(S^n) bounds, so that every cycle bounds, and then the homology is trivial.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Using Jordan Curve Thm to Show H_n(R^n) Trivial?

Loading...

Similar Threads - Using Jordan Curve | Date |
---|---|

I Notations used with vector field and dot product | Jan 22, 2017 |

I How to write the Frenet equations using the vector gradient? | Jun 24, 2016 |

How do I use the geodesic equation for locations on earth | Dec 19, 2015 |

Proof of Jordan-Brouwer Separation Theorem Using Homotopy Theory? | Jul 26, 2011 |

**Physics Forums - The Fusion of Science and Community**