User contributions
- 07:07, 10 January 2019 (diff | hist) N Talk:Uniqueness of contractible coboundary (Ex) (Created page with "<wikitex>; Let $Y^3$ be a homology $3$-sphere bounding contractible $4$-manifolds $\Omega_1^4$ and $\Omega_2^4$. Let $W:=\Omega_1\cup_{Y\times 0}(Y\times I)\cup_{Y\times 1}(-...") (top)
- 06:37, 10 January 2019 (diff | hist) N Talk:Representing homology classes by embedded 2-spheres (Ex) (Created page with "<wikitex>; 1. Let $M=8\mathbb{CP}^2\#\overline{\mathbb{CP}}^2$. In the previous exercise, we showed that the intersection form $8\langle 1\rangle\oplus\langle-1\rangle$ Of $M...") (top)
- 06:02, 10 January 2019 (diff | hist) N Talk:Integral homology 3-spheres embed in the 4-sphere (Ex) (Created page with "<wikitex>; Let $Y^3$ be a homology $3$-sphere. By Freedman, there exists a (unique) contractible topological $4$-manifold $\Omega^4$ with $\partial Y=\Omega$. Let $W:=\Omega...") (top)
- 02:24, 10 January 2019 (diff | hist) N Talk:Dual Thurston polytope of the 3-torus (Ex) (Created page with "<wikitex>; Let $\phi\in H^1(T^3;\mathbb{Z})$. Fix a basis $(x,y,z)$ of $H_1(T^3;\mathbb{Z})$. View $\phi$ as a map from $\mathbb{Z}^3$ to $\mathbb{Z}$. Then the kernel of $\p...") (top)
- 07:06, 9 January 2019 (diff | hist) Talk:Connected sum of topological manifolds (Ex) (Explained how to (ambiently) isotope the center of one ball to the other, in steps using charts) (top)
- 06:22, 9 January 2019 (diff | hist) Talk:Volume of a closed hyperbolic 3-manifold (Ex) (Changed “homotopy” to “homotopic”) (top)
- 06:22, 9 January 2019 (diff | hist) N Talk:Volume of a closed hyperbolic 3-manifold (Ex) (Created page with "<wikitex>; Let $M$ be a hyperbolic closed $3$-manifold. Let $N$ be another hyperbolic closed $3$-manifold with $\pi_1(M)\cong\pi_1(N)$. Since $M$ and $N$ are both hyperbolic...")
- 06:00, 9 January 2019 (diff | hist) N Talk:Elementary invariants of Heegaard diagrams (Ex) (Created page with "<wikitex>; The Heegaard diagram $(\Sigma_g,\alpha,\beta)$ naturally gives a handle structure on $Y$. The handlebody $H_\alpha$ consists of the $0$-handle and $g$ $1$-handles,...") (top)
- 04:22, 9 January 2019 (diff | hist) m Talk:Connected sum of topological manifolds (Ex) (Accidentally wrote 4 instead of n out of habit; fixed)
- 14:30, 8 January 2019 (diff | hist) Talk:Connected sum of topological manifolds (Ex) (Simplified base case of part 2)
- 09:55, 8 January 2019 (diff | hist) Talk:Connected sum of topological manifolds (Ex)
- 07:27, 8 January 2019 (diff | hist) m Talk:Connected sum of topological manifolds (Ex)
- 07:12, 8 January 2019 (diff | hist) m Talk:Euler characteristic as surgery obstruction (Ex) (top)
- 07:10, 8 January 2019 (diff | hist) N Talk:Euler characteristic as surgery obstruction (Ex) (Created page with "<wikitex>; If $n$ is odd, then $\chi(X)=\chi(M’)=\chi(M)=0$. So assume $n$ is even. We will check the effect surgery has on Euler characteristic. Let $S^k\subset M^n$ be a...")
- 05:58, 8 January 2019 (diff | hist) N Talk:Connected sum of topological manifolds (Ex) (Created page with "<wikitex>; Let $M^n$ be an (oriented) topological $n$-manifold. Choose any two embeddings $f,g:S^{n-1}\to M^n$ so that $f(S^{n-1})$ and $g(S^{n-1})$ bound topological balls i...")
- 02:13, 8 January 2019 (diff | hist) N Talk:Simple closed curves in surfaces (Ex) (Created page with "<wikitex>; Suppose that $S=\Sigma_g\setminus(\cup_{i=1}\nu(\alpha_i))$ is connected. We will construct a dual basis $\beta_1,...,\beta_g$ as usual and then use the intersectio...")
- 01:20, 8 January 2019 (diff | hist) N Talk:Atoroidal 3-manifolds (Ex) (Created page with "<wikitex>; No. $M$ could for example be a lens space or $S^1\times S^2$. We do know that because $\pi_1(M)$ doesn’t contain a copy of $\mathbb{Z}^2$, $M$ is atoroidal. Then...") (top)
- 09:13, 7 January 2019 (diff | hist) N User:Maggie Miller (Created page with "I am a 4th year Ph.D. Student at Princeton University, planning to graduate in spring 2020. My advisor is David Gabai. I am primarily interested in knots in dimensions three ...") (top)
- 09:07, 7 January 2019 (diff | hist) N Talk:Betti numbers of 3-manifolds (Ex) (Created page with "<wikitex>; Now let $M$ be a closed, orientable $3$-manifold with $\pi_1(M)=G$. View $M$ as a finite CW complex, with cells in dimensions-$0,1,2,3$, as usual. Attach cells of ...")