User Eric O. Korman - Mathematics Stack Exchange

69 votes

Conjectures that have been disproved with extremely large counterexamples?

answered Jul 22, 2010 at 20:59

68 votes

Best Algebraic Topology book/Alternative to Allen Hatcher free book?

answered Nov 22, 2011 at 3:36

68 votes

Accepted

Is the vector cross product only defined for 3D?

answered Aug 23, 2012 at 19:33

34 votes

Accepted

Fundamental group of the special orthogonal group SO(n)

answered Mar 23, 2012 at 16:28

23 votes

Accepted

Why is the orthogonal group $\operatorname{O}(2n,\mathbb R)$ not the direct product of $\operatorname{SO}(2n, \mathbb R)$ and $\mathbb Z_2$?

answered Mar 27, 2011 at 13:52

22 votes

Accepted

Is the determinant the "only" group homomorphism from $\mathrm{GL}_n(\mathbb R)$ to $\mathbb R^\times$?

answered Mar 26, 2014 at 4:25

20 votes

Accepted

What are defining & fundamental representations?

answered Jul 15, 2013 at 19:12

20 votes

No diffeomorphism that takes unit circle to unit square

answered Jul 28, 2011 at 0:55

19 votes

Accepted

Intuitive explanation of covariant, contravariant and Lie derivatives

answered Jul 28, 2010 at 23:10

19 votes

Surprising Generalizations

answered Aug 2, 2010 at 0:06

17 votes

Lie algebra of a quotient of Lie groups

answered Mar 28, 2011 at 1:27

17 votes

Why do people care about principal bundles?

answered Nov 6, 2012 at 13:19

16 votes

Accepted

Show the existence of a polynomial $f$ such that $T^{-1} = f(T)$ for an invertible linear operator $T.$

answered Aug 17, 2012 at 1:01

15 votes

Roadmap to study Atiyah–Singer index theorem

answered Feb 5, 2013 at 3:56

15 votes

Accepted

Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms?

answered Jul 21, 2010 at 19:48

15 votes

Accepted

Two Definitions of the Special Orthogonal Lie Algebra

answered Mar 7, 2013 at 17:51

15 votes

Accepted

Is the Structure Group of a Fibre Bundle Well-Defined?

answered Mar 25, 2013 at 14:18

14 votes

Accepted

Do all representations of finite groups have one-dimensional subrepresentations?

answered Sep 3, 2012 at 16:49

14 votes

$\Omega=x\;dy \wedge dz+y\;dz\wedge dx+z\;dx \wedge dy$ is never zero when restricted to $\mathbb{S^2}$

answered Dec 30, 2011 at 14:05

13 votes

Accepted

Does the group of Diffeomorphisms act transitively on the space of Riemannian metrics?

answered Apr 6, 2012 at 14:11

13 votes

Accepted

Showing a vector field is tangent to the 2-sphere

answered Jan 25, 2013 at 21:13

13 votes

Accepted

fundamental group of $U(n)$

answered Oct 27, 2012 at 14:39

13 votes

Good Physical Demonstrations of Abstract Mathematics

answered Jul 22, 2010 at 13:05

13 votes

Why are $3D$ transformation matrices $4 \times 4$ instead of $3 \times 3$?

answered Jul 21, 2010 at 14:20

12 votes

What's so "natural" about the base of natural logarithms?

answered Jul 27, 2010 at 20:58

12 votes

Accepted

How do I measure distance on a globe?

answered Jul 27, 2010 at 1:33

12 votes

Accepted

If $A$ is a subobject of $B$, and $B$ a subobject of $A$, are they isomorphic?

answered Jul 21, 2010 at 13:20

12 votes

Equivalence of Definitions of Principal $G$-bundle

answered May 22, 2013 at 12:17

11 votes

Accepted

Learning Roadmap for Borel - Weil - Bott Theorem

answered Jun 6, 2013 at 12:41

11 votes

Intuition behind $dx \wedge dy=-dy \wedge dx$

answered Nov 23, 2010 at 0:17

Stack Exchange Network

194 Answers

Conjectures that have been disproved with extremely large counterexamples?

Best Algebraic Topology book/Alternative to Allen Hatcher free book?

Is the vector cross product only defined for 3D?

Fundamental group of the special orthogonal group SO(n)

Why is the orthogonal group $\operatorname{O}(2n,\mathbb R)$ not the direct product of $\operatorname{SO}(2n, \mathbb R)$ and $\mathbb Z_2$?

Is the determinant the "only" group homomorphism from $\mathrm{GL}_n(\mathbb R)$ to $\mathbb R^\times$?

What are defining & fundamental representations?

No diffeomorphism that takes unit circle to unit square

Intuitive explanation of covariant, contravariant and Lie derivatives

Surprising Generalizations

Lie algebra of a quotient of Lie groups

Why do people care about principal bundles?

Show the existence of a polynomial $f$ such that $T^{-1} = f(T)$ for an invertible linear operator $T.$

Roadmap to study Atiyah–Singer index theorem

Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms?

Two Definitions of the Special Orthogonal Lie Algebra

Is the Structure Group of a Fibre Bundle Well-Defined?

Do all representations of finite groups have one-dimensional subrepresentations?

$\Omega=x\;dy \wedge dz+y\;dz\wedge dx+z\;dx \wedge dy$ is never zero when restricted to $\mathbb{S^2}$

Does the group of Diffeomorphisms act transitively on the space of Riemannian metrics?

Showing a vector field is tangent to the 2-sphere

fundamental group of $U(n)$

Good Physical Demonstrations of Abstract Mathematics

Why are $3D$ transformation matrices $4 \times 4$ instead of $3 \times 3$?

What's so "natural" about the base of natural logarithms?

How do I measure distance on a globe?

If $A$ is a subobject of $B$, and $B$ a subobject of $A$, are they isomorphic?

Equivalence of Definitions of Principal $G$-bundle

Learning Roadmap for Borel - Weil - Bott Theorem

Intuition behind $dx \wedge dy=-dy \wedge dx$