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XiaoXiao Zhen's user avatar
XiaoXiao Zhen's user avatar
XiaoXiao Zhen's user avatar
XiaoXiao Zhen
  • Member for 9 years, 7 months
  • Last seen more than 9 years ago
10 votes
1 answer
264 views

Show every $f_t$ is Morse for $t$ is sufficiently small

6 votes
1 answer
716 views

Show that the central circle $X$ in the open Mobius band has mod 2 intersection number $I_2(X,X)=1$

5 votes
1 answer
780 views

Prove that $\deg_2 (f) \equiv q \mod 2$

5 votes
1 answer
593 views

Show that if $X$ may be deformed into $Z$ then $X$ and $Z$ are cobordant.

4 votes
3 answers
1k views

Prove that any map $f\colon S^1 \to S^1$ mapping antipodal point to antipodal point has $\deg_2(f)=1$ by a direct computation.

2 votes
1 answer
1k views

Give an example of 2 non isomorphic regular tournament of the same order

2 votes
1 answer
965 views

Prove that nondegenerate zeros are isolated.

2 votes
1 answer
816 views

Prove that every odd cycle is $3$-choosable without using the fact that $\chi_l(G) \leq 1+ \Delta(G)$

2 votes
1 answer
541 views

Why the map $z→z+ \overline z^m $ has fixed point with local Lefschetz number $m$ at the the origin of C (m≥0)?

1 vote
0 answers
159 views

Show that at a zero $x$, the derivative $d(\vec v_x ) :T_x (X)→R^N$ actually carries $T_x (X)$ into itself.

1 vote
1 answer
581 views

sketch given region an its image under given mapping $2 \leq Im z \leq 5$ and $w=iz$

1 vote
1 answer
126 views

Prove that $f$ map a neighborhood of $Z$ diffeomorphically on to a neighborhood of $f(Z)$( more detail)

1 vote
0 answers
100 views

Show that $R^n -X$ has at most 2 connected component without using the Jordan-Brouwer theorem.

1 vote
1 answer
517 views

Prove that if $G$ is an nontrivial connected graph with at most 2 bridges, then there exists an orientation $D$

0 votes
1 answer
75 views

Prove that if $u$ and $v$ do not lie on a common cycle then $od(u)≠od(v)$

0 votes
0 answers
59 views

Describe the image of following map $w= \frac{1}{z}$ with $|z-\frac {1}{2}| \leq \frac {1}{2}$