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Dec
12
comment If a covering map has a section, is it a $1$-fold cover?
@Jason deVito I think there might be a typo in your solution
Dec
12
comment Infinitely sheeted covering spaces!
@JasonDeVito But since any covering space of a manifold has to be a manifold, wouldn't all the covering spaces of a connected sum of tori be homeomorphic to a connected sum of tori?
Dec
12
comment If a covering map has a section, is it a $1$-fold cover?
Ok. Maybe someone else could give a more thorough explanation!
Dec
12
comment If a covering map has a section, is it a $1$-fold cover?
@rschwieb yes,it cast doubt on my solution...I am no longer sure that what I said holds...maybe you could shed some light.
Dec
12
awarded  Commentator
Dec
12
comment If a covering map has a section, is it a $1$-fold cover?
@rschwieb I'm not sure i understand what you are implying?
Dec
12
revised If a covering map has a section, is it a $1$-fold cover?
added 66 characters in body
Dec
12
answered If a covering map has a section, is it a $1$-fold cover?
Dec
12
comment Infinitely sheeted covering spaces!
Yes you are correct. My topology seems to be rusty...in this case wouldn't the proper subgroup of the fundamental group of the connected sum of tori be infinite cyclic then? Since this corresponds to some cover of the connected sum of tori then it would answer the op's question I think.
Dec
12
answered Infinitely sheeted covering spaces!
Dec
7
awarded  Student
Dec
7
comment Constructible numbers
Just edited my post, right on time:)
Dec
7
awarded  Editor
Dec
7
revised Constructible numbers
added 104 characters in body
Dec
7
asked Constructible numbers
Nov
29
comment Spectral Theorem
@ Robert Israel: so is that all what the problem is asking? Namely to assert that the diagonal entries of the matrix A will be $\pm 1$ after diagonalization? It seems too simple!
Nov
29
comment Spectral Theorem
@ froggie: thanks! Regarding the question the only other thing I can get is that the matrix A will have real eigenvalues.
Nov
29
comment Spectral Theorem
Does it suffice to say something along the lines: since the matrix is symmetric and orthogonal, then the matrix A would be normal, so there is some orthogonal matrix P such that $P^tAP$ is a diagonal matrix whose entries are all 1s. Would this suffice or is it asking for more, sth else?? Thanks
Nov
29
comment Spectral Theorem
@gedgar: yes thats correct...however my trouble is on how to phrase my answer.