Attaching maps in a product of CW-complexes

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SUMMARY

The discussion focuses on finding differential operators in the product of CW complexes, specifically for the example of RP2 x S2. The participant identifies the individual cells of RP2 and S2 and seeks clarification on how these cells are attached in the product space. A reference to Theorem A.6 in Hatcher's book is provided as a valuable resource for understanding this concept. The inquiry highlights the need for clear explanations regarding the attachment of cells in complex topological structures.

PREREQUISITES
  • Understanding of CW complexes and their structure
  • Familiarity with differential operators in algebraic topology
  • Knowledge of the attachment process of cells in topological spaces
  • Basic comprehension of Hatcher's "Algebraic Topology" and its theorems
NEXT STEPS
  • Study Theorem A.6 in Hatcher's "Algebraic Topology" for insights on cell attachment
  • Explore differential operators in the context of CW complexes
  • Research examples of product spaces in algebraic topology
  • Learn about the homology and cohomology of products of CW complexes
USEFUL FOR

Mathematicians, topologists, and students studying algebraic topology, particularly those interested in the properties and applications of CW complexes and differential operators.

mrbohn1
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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.
 
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Thanks...I should have known it would be somewhere in Hatcher.
 

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