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Laz's user avatar
Laz's user avatar
Laz
  • Member for 10 years, 1 month
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9 votes
Accepted

Prove the quotient map of real projective n space is smooth

8 votes

Isometries of the sphere $\mathbb{S}^{n}$

8 votes
Accepted

Why are local diffeomorphisms between spheres are actually diffeomorphism

5 votes
Accepted

Question about the proof of Reeb's theorem in Milnor's Morse Theory

4 votes

Why the flat torus cannot be immersed in euclidean plane?

4 votes
Accepted

Why are these sets saturated open sets?

4 votes
Accepted

A difficulty in understanding a part of solution of Q.1.3.10 in Allan Pollack and Guillemin.

4 votes
Accepted

$A=\Big\{f \in C[0,1]: f(x)\neq 0,\forall x \in [0,1]\Big\}$ is open in $C[0,1]$

4 votes
Accepted

Probability 3 points are collinear

3 votes
Accepted

How many zero divisors are there in $\mathbb Z_{pq}$ and $\mathbb Z_{p^2}$ when $p$ and $q$ are primes?

3 votes

Riemannian distance via exponential map

2 votes
Accepted

Gauss Lemma, Chapter 3 - Do Carmo's differential geometry.

2 votes
Accepted

Diffeomorphism and bracket?

2 votes

Given a surface $z=f(x,y)$ is $\nabla (f(a,b))$ always perpendicular to the surface at the point $(a,b,f(a,b))$

2 votes
Accepted

Why the 'gradient of the diffeomorphism at a point in the surface' perpendicular to the surface at that point?

2 votes

Computation of the fundamental group of the projective plane without Van Kampen theorem.

2 votes

Clarification on definition of smooth map between smooth manifolds

2 votes
Accepted

Composition Of A Non-Diffeomorphism And A Diffeomorphism

2 votes
Accepted

example of a sequence $x_n$ such that the set of limit points of $x_n$ is $[0,1]$.

2 votes
Accepted

Open and Closed maps in topology atan example

2 votes

Is $S^2 \times S^2$ diffeomorphic to $S^1 \times S^3$?

2 votes
Accepted

What does "an immersed sub manifold is in general not a submanifold as a subset" mean?

2 votes
Accepted

Relation between two different definitions of "regular surface"

2 votes
Accepted

Show that there are at least two points on a manifold to which a vector is normal

1 vote

Let $M$ be a $n$-dim manifold. If $f : M \to \mathbb{R}$ then does $\ker(df_p) = T_p(f^{-1}(c))$ for some $c \in f[M]$

1 vote
Accepted

Showing a subset is a submanifold of $T^2$

1 vote
Accepted

Image of this curve is contained in the ray if and only if v is an eigenvector of A

1 vote

Prove that $2p+1$ is a divisor of $2^p-1$

1 vote
Accepted

A difficulty in the proof of partial converse I.(p. 24 in Guillemin & Pollack)

1 vote

If $p|(a-b)$ and $q|(a-b)$, then prove that $pq|(a-b)$