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What is the difference between “Product” and “Twisted product”?

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0

$begingroup$

I am reading Allen Hatcher's book of Vector bundle and K-theory. Here I have gotten that :

"Mobius band is the twisted product of a circle and a
line. On the other hand annulus the product of a circle and a line."

My question is : What is the difference between "Product" and "Twisted product" ?

Also, what kind of objects are participants in "Twisted Product"? (groups, rings, fields, topological spaces or smooth manifolds?)

Thank you in advance.

Any reference or any lecture note can also help me.

differential-geometry algebraic-topology tensor-products products

share|cite|improve this question

asked Mar 11 at 9:05

BijanDattaBijanDatta

307113

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  The Mobius band is a real line bundle over the circle. When you read Hatcher's later discussion of the clutching construction his words here will make more immediate sense.
  $endgroup$
  – Tyrone
  Mar 11 at 11:17
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In Topology "a twisted product" is a way of intuitively thinking about Fibre Bundles. It's not a term that many people use officially.
  $endgroup$
  – William
  Mar 11 at 17:32
  

  
  
  
  

add a comment | 

0

$begingroup$

I am reading Allen Hatcher's book of Vector bundle and K-theory. Here I have gotten that :

"Mobius band is the twisted product of a circle and a
line. On the other hand annulus the product of a circle and a line."

My question is : What is the difference between "Product" and "Twisted product" ?

Also, what kind of objects are participants in "Twisted Product"? (groups, rings, fields, topological spaces or smooth manifolds?)

Thank you in advance.

Any reference or any lecture note can also help me.

differential-geometry algebraic-topology tensor-products products

share|cite|improve this question

asked Mar 11 at 9:05

BijanDattaBijanDatta

307113

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  The Mobius band is a real line bundle over the circle. When you read Hatcher's later discussion of the clutching construction his words here will make more immediate sense.
  $endgroup$
  – Tyrone
  Mar 11 at 11:17
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In Topology "a twisted product" is a way of intuitively thinking about Fibre Bundles. It's not a term that many people use officially.
  $endgroup$
  – William
  Mar 11 at 17:32
  

  
  
  
  

add a comment | 

$begingroup$

I am reading Allen Hatcher's book of Vector bundle and K-theory. Here I have gotten that :

"Mobius band is the twisted product of a circle and a
line. On the other hand annulus the product of a circle and a line."

My question is : What is the difference between "Product" and "Twisted product" ?

Also, what kind of objects are participants in "Twisted Product"? (groups, rings, fields, topological spaces or smooth manifolds?)

Thank you in advance.

Any reference or any lecture note can also help me.

differential-geometry algebraic-topology tensor-products products

share|cite|improve this question

asked Mar 11 at 9:05

BijanDattaBijanDatta

307113

$endgroup$

share|cite|improve this question

asked Mar 11 at 9:05

BijanDattaBijanDatta

307113

share|cite|improve this question

asked Mar 11 at 9:05

BijanDattaBijanDatta

307113

asked Mar 11 at 9:05

BijanDattaBijanDatta

307113

asked Mar 11 at 9:05

BijanDattaBijanDatta

307113