2
votes
1answer
171 views
Differentiable manifolds by Serge Lang question
I have started reading "Introduction to differentiable manifolds" by Serge Lang. In this book, Lang takes a different approach, by immediately introducing manifolds on arbitrary Ba …
1
vote
0answers
64 views
Topological classification of a real-valued functions on manifold
What is a motivation to study topological conjugacy of a real-valued functions on a manifold? (The importance of notion of a topologically conjugate homeomorphisms is clear for me) …
0
votes
0answers
54 views
Proving the vector field is transverse to M [closed]
Rather, let us consider tahat
21
votes
2answers
488 views
Vector fields on $(4n+1)$-spheres
If $n$ is odd then $S^{n-1}$ doesn't admit a nowhere-vanishing vector field, and if $n$ is even then there does exist one (Hairy Ball Theorem). We can then ask, on $S^{n-1}$, what …
1
vote
2answers
186 views
What does it mean that homotopy is generic?
Due to Cerf, there's exist a certain homotopy between two Morse functions. It is said that this homotopy is "generic". What is a precise definition of the property to be "generic" …
15
votes
4answers
726 views
Why are currents named currents?
Why do currents, functionals on compactly supported differentiable n-forms, bear the name they do?
I've assumed that it has something to do with an electrical current being formal …
2
votes
0answers
88 views
Uniqueness of the Smooth Structure on a Handle Attachment
I posted this question on math stack exchange and didn't receive an answer. If it is too elementary for this forum I will be happy to delete it.
Let $M^m$ be a smooth manifold wi …
5
votes
1answer
316 views
Cancellation law for $M^n\times \mathbb R= N^n\times \mathbb R$.
Assume $M^n$ and $N^n$ are null bordant, i.e. each can be realized as boundary of an $n+1$ dimensional manifold. Suppose $M^n \times \mathbb R$ is homeomorphic to $N^n\times \mathb …
0
votes
1answer
131 views
How to compute difference between 2 similarity matrices?
Hello,
I have two n*n correlation matrices with values ranging between -1,1. (2 correlation matrix because I have the same n terms under 2 different conditions)
I then transformed …
7
votes
2answers
245 views
Sum of two tangent bundles of $S^{2n}$
I was wondering if the sum $TS^{2n}\oplus TS^{2n}$ is a trivial bundle?
The same is true for spheres of odd dimension (one can find a nowhere zero section of the second bundle, add …
13
votes
3answers
552 views
4D TQFT from a modular tensor category
I know the construction of a 3D topological quantum field theory (TQFT) from a modular tensor category.
I heard that we can even (mathematically) construct 4D TQFT from a modular …
5
votes
2answers
325 views
Quotient of trivial bundles
Suppose you are on a manifold. Suppose you have a trivial bundle and a trivial subbundle of it. If you divide this trivial bundle with its trivial subbundle, do you get a trivial b …
3
votes
1answer
85 views
Smooth function algebra on cartesian product and beyond
Short question:
Let $M$ and $N$ be smooth manifold, with appropriate smooth function algebras
$C^\infty(M,\mathbb{R})$ and $C^\infty(N,\mathbb{R})$.
Can we express the smooth fu …
2
votes
1answer
246 views
Is the space of gradient-like vector fields contractible?
Let $M$ be a compact manifold (without boundary) and let $f:M\to \mathbb{R}$ be a fixed Morse-function.
Question: Is the space $GVect(M,f)$ of all gradient-like vector-fields f …
1
vote
0answers
87 views
Orbits and indices of vector fields
I'm afraid this might be an exercise in differential topology (in which case a reference to a book where it is would be very much appreciated); apologies in advance. Given an analy …

