I am wondering if the following mod 2 cohomology class which can be defined on any compact surface, has any geometric meaning or is important in any way.(adsbygoogle = window.adsbygoogle || []).push({});

triangulate the surface then take the first barycentric subdivision. This is a new triangulation.

Define a 1 - cochain on this new triangulation as 1 on any 1- simplex that touches the barycenter of one of the 2 - simplices in the original triangulation and zero on any other 1 simplex. This is a mod 2 cocycle which is easily seen by drawing a picture.

I wonder if this is the first Stiefel-Whitney class of the surface.

**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!

# A cohomology class on surfaces

Loading...

Similar Threads - cohomology class surfaces | Date |
---|---|

I Cohomology ring | Nov 5, 2017 |

A Is there a natural paring between homology and cohomology? | Feb 12, 2017 |

A Very basic question about cohomology. | Jan 25, 2017 |

Extending a d-cohomology class to D-cocycle | Nov 12, 2011 |

Why does Chern class belong to INTEGER cohomology class? | Aug 18, 2010 |

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