Jump to content

File:Simplicial homology - exactness of boundary maps.svg

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (SVG file, nominally 260 × 325 pixels, file size: 7 KB)

Summary

Description
English: The boundary of the boundary of a 2-simplex (left) and the boundary of a 1-chain (right) are taken. The boundary of a boundary is always trivial, always sums to 0. A nontrivial cycle is something that closes up like the boundary of a simplex, in that its boundary is 0, but which isn't actually the boundary of a simplex or chain. Two cycles are homologous when their difference is a boundary, and in that sense two closed paths are equivalent if one can turn one into the other by passing through a solid region.
Date
Source Own work
Author Loki Clock

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

10 February 2014

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current20:28, 10 February 2014Thumbnail for version as of 20:28, 10 February 2014260 × 325 (7 KB)LokiClockWould have to be direct sums of ZZ not direct products to not be misleading, but that would be too big to write in the same place and anyway this is only an isomorphic description, so using the chain groups instead is best.
19:28, 10 February 2014Thumbnail for version as of 19:28, 10 February 2014260 × 325 (7 KB)LokiClockFix masking using suggestions of "http://sourceforge.net/mailarchive/message.php?msg_id=31781270".
17:36, 10 February 2014Thumbnail for version as of 17:36, 10 February 2014260 × 325 (7 KB)LokiClockUser created page with UploadWizard

The following 2 pages use this file:

Global file usage

The following other wikis use this file:

Metadata