Attaching maps in a product of CW-complexes

  • Thread starter mrbohn1
  • Start date
  • Tags
    Product
In summary, to find the differential operators in a product of CW complexes, where the individual differential operators are known, one can refer to theorem A.6 in the appendix of Hatcher's book. This includes a link to the appendix which provides further explanation and examples.
  • #1
mrbohn1
97
0
Could someone please explain to me how to find the differential operators in a product of CW complexes, if the individual differential operators are known?

For example, I know that RP2x S2 has 1 0-cell, 1 1-cell, 1 2- cells and 1 4-cell, and I know how the cells of RP2 and S2 are attached, but I don't know how the cells of RP2 x S2 are attached.

I'd be happy with a link to somewhere that explains this, I haven't been able to find a source. Thanks.
 
Physics news on Phys.org
  • #3
Thanks...I should have known it would be somewhere in Hatcher.
 

Related to Attaching maps in a product of CW-complexes

1. What is the purpose of attaching maps in a product of CW-complexes?

The purpose of attaching maps in a product of CW-complexes is to construct a new CW-complex by combining multiple existing CW-complexes together in a specific way. This allows for a more efficient and organized representation of a larger space.

2. How is the attaching map determined?

The attaching map is determined by specifying the attaching maps for each individual CW-complex that is being combined. These attaching maps must satisfy certain conditions in order to ensure that the resulting product is a valid CW-complex.

3. Can attaching maps be used to construct any type of space?

No, attaching maps can only be used to construct CW-complexes. These are topological spaces that are built from simpler pieces called cells, and are commonly used to study algebraic topology and homotopy theory.

4. Are there any limitations to how many CW-complexes can be combined using attaching maps?

There are no limitations on the number of CW-complexes that can be combined using attaching maps. However, the resulting product will only be a valid CW-complex if the attaching maps are carefully chosen and satisfy the necessary conditions.

5. What are the benefits of using attaching maps in constructing CW-complexes?

Attaching maps allow for a more efficient and systematic way of constructing CW-complexes. They also provide a way to study the structure and properties of a larger space by breaking it down into simpler components. Additionally, attaching maps can be used to construct more complex spaces by combining simpler ones.

Similar threads

Manually charging batteries
    • Electrical Engineering
Replies
11
Views
333
I Question regarding the 3-form ##dx^i \wedge dx^j \wedge dx^k##
    • Differential Geometry
Replies
13
Views
579
I Visualization of complex vectors and dot product
    • Linear and Abstract Algebra
Replies
14
Views
769
How does gene regulation result in differentiation of different organs?
    • Biology and Medical
Replies
3
Views
1K
COVID Precisely how does Pfizer's Covid-19 mRNA vaccine work?
    • Biology and Medical
Replies
31
Views
5K
Interesting Path to Eukaryotic Cell Complexity Proposed
    • Biology and Medical
Replies
4
Views
1K
I Does a Fabry Perot cavity charge in discrete steps?
    • Optics
Replies
12
Views
1K
Pre-Eukaryotic Cells of the Asgard Superphylum Cultured in Japan
    • Biology and Medical
Replies
6
Views
3K
Comp Sci Complexity for generating strings of length k from CNF grammar
    • Engineering and Comp Sci Homework Help
Replies
3
Views
972
me Translate French Math Terms
    • Differential Geometry
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top