Kelvin Lois's user avatar
Kelvin Lois's user avatar
Kelvin Lois's user avatar
Kelvin Lois
  • Member for 7 years, 11 months
  • Last seen this week
  • Jakarta, Indonesia
9 votes
0 answers
379 views

Homeomorphism between $[0,\infty)^n$ with Upper Half-Space $\mathbb{H}^n$ [duplicate]

8 votes
3 answers
1k views

Neighbourhood of Linearly Independent Vector Fields $(X_1,\dots,X_n)$

7 votes
2 answers
2k views

Finding local orthonormal frame on a Pseudo-Riemannian Manifold

7 votes
1 answer
1k views

Intersection of two Lie subgroup is Lie subgroup ?

5 votes
1 answer
627 views

Show that the total space $E$ of a fibre bundle $\pi : E \rightarrow M$ is connected.

5 votes
1 answer
442 views

Open subsets of the connected sum $M_1\# M_2$ [duplicate]

5 votes
1 answer
788 views

Proof that Connection is local operator.

5 votes
2 answers
2k views

An Example of a Torsion Module

5 votes
1 answer
402 views

Poincare Duality in Morse Homology

4 votes
1 answer
169 views

Continuity of retraction on $r : \text{Int }\Omega^c \to B$

4 votes
0 answers
457 views

Using bump function in coordinate chart to construct a vector field $V$ along a curve $\gamma$ with particular properties.

3 votes
2 answers
410 views

Connection on vector bundle : Prove that $(\nabla_X Y)(p)=0$ if $X(p)=0$.

3 votes
1 answer
332 views

Countable and Uncountable cover in Partition of Unity Arguments

2 votes
0 answers
233 views

Why limit map induces isomorphisms of homotopy groups of all dimensions?

2 votes
1 answer
659 views

Subset of Open submanifold is a submanifold?

2 votes
0 answers
174 views

Neighbourhood of a point where $(\theta_1)_{t_1} \circ (\theta_2)_{t_2} \circ \cdots \circ (\theta_k)_{t_k}$ is defined

2 votes
4 answers
124 views

If $S,T : V \to V$ are linear maps such that $\text{Im}\, S \subseteq \text{Im}\,T$, find $R : V \to V$ such that $S = T \circ R$.

2 votes
0 answers
185 views

Symmetric bilinear from $(d^2g)_x$ is well-defined on $\text{Ker}(dg)_x \subset T_xM$?

2 votes
2 answers
184 views

Possible correction for Theorem 6.13 (Hopf-Rinow) Lee's book Riemannian Manifold 2nd Ed?

2 votes
2 answers
912 views

The closure of a subset in finer topology is always subset of the closure of that subset in the coarser one.

2 votes
1 answer
1k views

Extending Local Smooth Function $f : U\subset M \rightarrow \mathbb{R}$

2 votes
1 answer
266 views

Show that $G/2G \cong (\mathbb{Z}/2)^n$, where $G$ is an abelian group and $G \cong \mathbb{Z}^n$

2 votes
2 answers
926 views

Show that $CX$ is locally (path-)connected iff $X$ is

2 votes
0 answers
398 views

Extension of Inverse Function Theorem to Manifold with Boundary

1 vote
0 answers
434 views

Show that if $dF_p$ is nonsingular, then $F(p)\in \text{Int}N$ : Lee's Smooth Manifolds

1 vote
0 answers
1k views

Using Gluing Lemma for Smooth Functions

1 vote
1 answer
215 views

Interpretation of Riemannian metric $g : M \rightarrow T^2(T^*M)$ on a smooth curve $\gamma : I \rightarrow M$.

1 vote
0 answers
161 views

Exercise on The Definition of Tangent Vector via Curve (Jeffrey Lee)

1 vote
1 answer
121 views

Details Related to One-variable Calculus in a proof of Morse Lemma.

1 vote
1 answer
145 views

A linear algebra related detail in a proof of Index Theorem