User Jesse Madnick - Mathematics Stack Exchange

221 votes

5 answers

25k views

What do modern-day analysts actually do?

asked Dec 28, 2011 at 4:13

65 votes

2 answers

8k views

How do different definitions of "degree" coincide?

asked May 2, 2012 at 22:12

63 votes

4 answers

6k views

Why is the Laplacian important in Riemannian geometry?

asked Feb 1, 2014 at 5:43

43 votes

1 answer

5k views

What is magical about Cartan's magic formula?

asked Aug 30, 2012 at 2:00

40 votes

8 answers

4k views

Why do we care about two subgroups being conjugate?

asked Dec 18, 2015 at 8:47

37 votes

4 answers

3k views

Geometry or topology behind the "impossible staircase"

asked Jul 14, 2011 at 22:26

33 votes

1 answer

7k views

Classifying the compact subsets of $L^p$

asked Apr 26, 2011 at 1:13

32 votes

3 answers

7k views

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

asked Jun 23, 2011 at 7:58

30 votes

2 answers

3k views

Equivalence of Definitions of Principal $G$-bundle

asked May 22, 2013 at 9:24

25 votes

4 answers

3k views

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

asked Feb 5, 2013 at 9:49

23 votes

2 answers

2k views

Why study "curves" instead of 1-manifolds?

asked Dec 5, 2010 at 21:53

21 votes

3 answers

11k views

Compactness in the weak* topology

asked Mar 16, 2011 at 16:59

20 votes

2 answers

1k views

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

asked Jan 11, 2011 at 4:29

18 votes

4 answers

3k views

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

asked Sep 13, 2011 at 23:16

17 votes

2 answers

1k views

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

asked Sep 27, 2010 at 18:22

17 votes

1 answer

975 views

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

asked Jun 14, 2014 at 2:38

15 votes

2 answers

2k views

Are there higher-dimensional analogues of sectional curvature?

asked Aug 16, 2010 at 0:39

15 votes

1 answer

3k views

How to apply Stokes' Theorem for manifolds with boundary

asked May 15, 2011 at 22:06

13 votes

2 answers

3k views

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

asked Sep 27, 2010 at 18:25

13 votes

2 answers

1k views

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

asked Feb 29, 2016 at 7:12

12 votes

1 answer

856 views

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

asked Feb 2, 2019 at 5:23

11 votes

1 answer

395 views

Why are diffeomorphism-invariant PDE not elliptic?

asked May 12, 2015 at 7:15

11 votes

3 answers

803 views

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

asked Feb 21, 2011 at 1:33

11 votes

2 answers

2k views

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

asked Jul 21, 2011 at 9:03

11 votes

2 answers

1k views

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

asked Oct 27, 2011 at 20:47

11 votes

2 answers

549 views

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

asked Jun 26, 2013 at 2:52

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?

asked Oct 27, 2013 at 8:47

10 votes

2 answers

676 views

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

asked Mar 2, 2013 at 5:46

10 votes

2 answers

400 views

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

asked Dec 25, 2010 at 9:53

9 votes

0 answers

295 views

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

asked Apr 28, 2018 at 0:54

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48 Questions

What do modern-day analysts actually do?

How do different definitions of "degree" coincide?

Why is the Laplacian important in Riemannian geometry?

What is magical about Cartan's magic formula?

Why do we care about two subgroups being conjugate?

Geometry or topology behind the "impossible staircase"

Classifying the compact subsets of $L^p$

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

Equivalence of Definitions of Principal $G$-bundle

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

Why study "curves" instead of 1-manifolds?

Compactness in the weak* topology

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

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

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

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

Are there higher-dimensional analogues of sectional curvature?

How to apply Stokes' Theorem for manifolds with boundary

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

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

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

Why are diffeomorphism-invariant PDE not elliptic?

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

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

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

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

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

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

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

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