Help with 'connected sum" symbol #

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In summary, the conversation is about the use of the symbol # in latex for the connected sum of two projective planes. One person had trouble using the symbol, but another provided a solution and a helpful link to a list of latex symbols.
  • #1
Math Amateur
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I just completed a post in the Topology and Advanced Geometry forum regarding the connected sum of two projective planes.

I wanted to use the symbol # for the connected sum as is usual in the topology books I am studying - but just typing in the symbol 'upsets' latex and so my post cannot be read!

Can someone please tell me how to produce the symbol # in latex?

Peter
 
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  • #2
$\#$
 
  • #3
Evgeny.Makarov said:
$\#$
Thanks Evgeny ... so it is \# ...

Thanks again,

Peter
 
  • #4
This is true of a number of important symbols in $\LaTeX$: $\$$, $\#$, $\&$, $\%$, $\_$, $\{$, $\}$. For a rather exhaustive, and possibly exhausting, list of $\LaTeX$ symbols, go here.
 
  • #5
Ackbach said:
This is true of a number of important symbols in $\LaTeX$: $\$$, $\#$, $\&$, $\%$, $\_$, $\{$, $\}$. For a rather exhaustive, and possibly exhausting, list of $\LaTeX$ symbols, go here.

Superb link there, Ackbach! Thanks for sharing! (Handshake)
 

1. What is the "connected sum" symbol # used for?

The "connected sum" symbol # is used in topology to denote the operation of connecting two manifolds together along a boundary. It represents the formation of a new, larger manifold by gluing two manifolds together along their common boundary.

2. How is the "connected sum" symbol # written mathematically?

In mathematical notation, the "connected sum" symbol # is written as M # N, where M and N are the two manifolds being connected. This is typically followed by a subscript number to indicate the number of connected sums being performed.

3. Can the "connected sum" symbol # be used with any two manifolds?

No, the "connected sum" operation can only be performed on manifolds of the same dimension. For example, a 2-dimensional manifold can only be connected to another 2-dimensional manifold, not a 3-dimensional one.

4. How is the "connected sum" symbol # different from the Cartesian product symbol x?

The "connected sum" symbol # is different from the Cartesian product symbol x because it creates a new, single manifold by gluing two manifolds together, while the Cartesian product results in a product manifold with two separate components.

5. Are there any rules or properties associated with the "connected sum" symbol #?

Yes, there are several rules and properties associated with the "connected sum" symbol #, such as associativity (the order in which the connected sums are performed does not matter) and commutativity (swapping the order of the manifolds being connected does not change the resulting manifold). Additionally, the resulting manifold may have different properties depending on the properties of the original manifolds being connected.

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