## Tagged Questions

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 …
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) …
0answers
54 views

### Proving the vector field is transverse to M [closed]

Rather, let us consider tahat
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 …
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" …
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 …
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 …
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 …
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 …
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 …
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 …
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 …
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 …
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 …
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 …

15 30 50 per page
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.905379593372345, "perplexity_flag": "middle"}