Simplicial volume
(Difference between revisions)
(Undo revision 2195 by Diarmuid Crowley (Talk)) |
|||
Line 1: | Line 1: | ||
− | {{Authors|Crowley}} | + | <!-- COMMENT: |
+ | |||
+ | To achieve a unified layout, along with using the template below, please OBSERVE the following: besides, $...$ and $$...$$, you should use two environments: | ||
+ | |||
+ | - For statements like Theorem, Lemma, Definition etc., use e.g. | ||
+ | {{beginthm|Theorem 1|(Milnor)}} ... ... ... {{endthm}}. | ||
+ | |||
+ | - For references, use e.g. {{cite|Milnor1958b}}. | ||
+ | |||
+ | DON'T FORGET TO ENTER YOUR USER NAME INTO THE {{Authors| }} TEMPLATE BELOW. | ||
+ | |||
+ | END OF COMMENT | ||
+ | Clara Löh | ||
+ | -->{{Authors|Crowley}} | ||
== Definition and history == | == Definition and history == | ||
<wikitex>; | <wikitex>; |
Revision as of 12:48, 10 March 2010
An earlier version of this page was published in the Bulletin of the Manifold Atlas: screen, print. You may view the version used for publication as of 09:51, 1 April 2011 and the changes since publication. |
The user responsible for this page is Crowley. No other user may edit this page at present. |
1 Definition and history
Definition 1.1. Let be an oriented closed connected manifold of dimension . Then the simplicial volume (also called Gromov norm) of is defined as
Here, denotes the singular chain complex of with real coefficients, and denotes the -norm on the singular chain complex induced from the (unordered) basis given by all singular simplices; i.e., for a chain (in reduced form), the -norm of is given by
2 References
This page has not been refereed. The information given here might be incomplete or provisional. |