Jesse Madnick's user avatar
Jesse Madnick's user avatar
Jesse Madnick's user avatar
Jesse Madnick
  • Member for 13 years, 6 months
  • Last seen this week
218 votes
5 answers
24k views

What do modern-day analysts actually do?

64 votes
2 answers
7k views

How do different definitions of "degree" coincide?

61 votes
4 answers
5k views

Why is the Laplacian important in Riemannian geometry?

42 votes
1 answer
4k views

What is magical about Cartan's magic formula?

40 votes
8 answers
4k views

Why do we care about two subgroups being conjugate?

37 votes
4 answers
3k views

Geometry or topology behind the "impossible staircase"

33 votes
1 answer
7k views

Classifying the compact subsets of $L^p$

32 votes
3 answers
7k views

Geometric interpretation of connection forms, torsion forms, curvature forms, etc

27 votes
2 answers
3k views

Equivalence of Definitions of Principal $G$-bundle

25 votes
4 answers
2k views

Are the Ricci and Scalar curvatures the only "interesting" tensors coming from the Riemannian curvature tensor?

22 votes
2 answers
2k views

Why study "curves" instead of 1-manifolds?

21 votes
3 answers
11k views

Compactness in the weak* topology

20 votes
2 answers
1k views

Diffeomorphic, group-isomorphic Lie groups that are not isomorphic as Lie groups

18 votes
4 answers
3k views

Texts on Principal Bundles, Characteristic Classes, Intro to 4-manifolds / Gauge Theory

17 votes
2 answers
1k views

When does the topological boundary of an embedded manifold equal its manifold boundary?

17 votes
1 answer
950 views

Is every scalar differential operator on $(M,g)$ that commutes with isometries a polynomial of the Laplacian?

15 votes
2 answers
2k views

Are there higher-dimensional analogues of sectional curvature?

15 votes
1 answer
3k views

How to apply Stokes' Theorem for manifolds with boundary

13 votes
2 answers
3k views

Classification Theorem for Non-Compact 2-Manifolds? 2-Manifolds With Boundary?

12 votes
2 answers
998 views

How is the smoothness of the space of deformations related to unobstructedness?

12 votes
1 answer
804 views

Does every non-compact Riemann surface embed holomorphically into $\mathbb{C}^2$?

11 votes
1 answer
385 views

Why are diffeomorphism-invariant PDE not elliptic?

11 votes
3 answers
766 views

What is $T\mathbb{S}^2$?

11 votes
2 answers
2k views

What are all topological spaces obtained by gluing the edges of a triangle?

11 votes
2 answers
1k views

Why do horizontal curves have zero covariant derivative along their projection?

11 votes
2 answers
538 views

Can we smoothly embed $\mathbb{S}^2 \times \mathbb{S}^1$ or $\mathbb{RP}^2 \times \mathbb{R}$ in $\mathbb{R}^4$?

10 votes
1 answer
1k views

How does a left group action on the fiber of a principal bundle induce a right action on the total space?

10 votes
2 answers
666 views

Which coefficients of the characteristic polynomial of the shape operator are isometric invariants?

10 votes
2 answers
385 views

What are some examples of $\text{Isom}(M)$ and $\text{Conf}(M)$?

9 votes
0 answers
294 views

Calculating the Ring of Invariant Polynomials for the Action of a Compact Simple Lie Group