Fdtxjr

What should you do if you miss a job interview (deliberately)?

Why is the "ls" command showing permissions of files in a FAT32 partition?

Why should universal income be universal?

What if a revenant (monster) gains fire resistance?

Does Doodling or Improvising on the Piano Have Any Benefits?

Yosemite Fire Rings - What to Expect?

Can I still be respawned if I die by falling off the map?

Pre-mixing cryogenic fuels and using only one fuel tank

How can "mimic phobia" be cured or prevented?

Fear of getting stuck on one programming language / technology that is not used in my country

Angel of Condemnation - Exile creature with second ability

Can a Canadian Travel to the USA twice, less than 180 days each time?

Is aluminum electrical wire used on aircraft?

Unexpected behavior of the procedure `Area` on the object 'Polygon'

How do you make your own symbol when Detexify fails?

Can a College of Swords bard use a Blade Flourish option on an opportunity attack provoked by their own Dissonant Whispers spell?

How do apertures which seem too large to physically fit work?

How does the math work for Perception checks?

Can a stoichiometric mixture of oxygen and methane exist as a liquid at standard pressure and some (low) temperature?

How could a planet have erratic days?

Why does a simple loop result in ASYNC_NETWORK_IO waits?

Mimic lecturing on blackboard, facing audience

Non-trope happy ending?

Multiplicative persistence

let c be a k cube, prove that there exists no k+1 chain b such that $partial b = c$

Proof and counter-example that a chain $c_R, n ne partial c$. Where is the error?Integrating differential form questionproperty of sum of coefs of a chainProblem from spivak's calculus singular cubessingular $1$ cube - Boundary of $2$ chainProof that exact form are path independent seems to imply the same for merely closed formsQuestion about Lee's Introduction to Smooth Manifolds (2 ed.) problem 18-1Show that $mathbbS^d$ is homeomorphic to the the boundary of the cube $partial I^d+1$.Trying to prove $partial^2=0$ on $k$-cellsQuestion on the proof of Stokes' Theorem in Spivak

1

$begingroup$

There is a former question says we can define the boundary of b as a certain linear combination of k-cubes, $partial b = sum_i a_i c_i$, prove $sum_i a_i = 0$, where $c_i$ are k-cubes, if I can show this, then it follows that $partial b$ cannot be a cube, but I have no idea how to show $sum_i a_i = 0$.
And I know the boundary of boundary is 0, so if $partial b = c$, then $partial c = 0$, which means $int_c da = int_partial c a = 0$ for any k-1 form a, and how can I make a contradiction from here. Thank you for any help.

multivariable-calculus differential-geometry

share|cite|improve this question

asked Mar 15 at 4:06

Ziqin HeZiqin He

232

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It would really help to give a link to this earlier question....
  $endgroup$
  – Lord Shark the Unknown
  Mar 15 at 4:58
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Lord Shark the Unknown Emm, the earlier question is also in the book Manifolds and Differential Forms together with this question and not on the website, sorry for my inaccurate expression
  $endgroup$
  – Ziqin He
  Mar 15 at 5:39
  

  
  
  
  

add a comment | 

1

$begingroup$

There is a former question says we can define the boundary of b as a certain linear combination of k-cubes, $partial b = sum_i a_i c_i$, prove $sum_i a_i = 0$, where $c_i$ are k-cubes, if I can show this, then it follows that $partial b$ cannot be a cube, but I have no idea how to show $sum_i a_i = 0$.
And I know the boundary of boundary is 0, so if $partial b = c$, then $partial c = 0$, which means $int_c da = int_partial c a = 0$ for any k-1 form a, and how can I make a contradiction from here. Thank you for any help.

multivariable-calculus differential-geometry

share|cite|improve this question

asked Mar 15 at 4:06

Ziqin HeZiqin He

232

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It would really help to give a link to this earlier question....
  $endgroup$
  – Lord Shark the Unknown
  Mar 15 at 4:58
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Lord Shark the Unknown Emm, the earlier question is also in the book Manifolds and Differential Forms together with this question and not on the website, sorry for my inaccurate expression
  $endgroup$
  – Ziqin He
  Mar 15 at 5:39
  

  
  
  
  

add a comment | 

$begingroup$

There is a former question says we can define the boundary of b as a certain linear combination of k-cubes, $partial b = sum_i a_i c_i$, prove $sum_i a_i = 0$, where $c_i$ are k-cubes, if I can show this, then it follows that $partial b$ cannot be a cube, but I have no idea how to show $sum_i a_i = 0$.
And I know the boundary of boundary is 0, so if $partial b = c$, then $partial c = 0$, which means $int_c da = int_partial c a = 0$ for any k-1 form a, and how can I make a contradiction from here. Thank you for any help.

multivariable-calculus differential-geometry

share|cite|improve this question

asked Mar 15 at 4:06

Ziqin HeZiqin He

232

$endgroup$

share|cite|improve this question

asked Mar 15 at 4:06

Ziqin HeZiqin He

232

share|cite|improve this question

asked Mar 15 at 4:06

Ziqin HeZiqin He

232

asked Mar 15 at 4:06

Ziqin HeZiqin He

232

asked Mar 15 at 4:06

Ziqin HeZiqin He

232