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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.