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Jan
31
asked Homology with local coefficients in a $\mathbb{Z}[\pi_1(X)]$-module
Jan
27
comment Does there exist a surface homemomorphic to a torus with positive Gaussian curvature?
@Felipe: any compact surface in $\mathbb{R}^3$ has a point with positive curvature. Indeed, it is bounded, thus it lies inside of a big enough sphere. Now reduce the sphere's radio until it first touches the surface in a point. That point of the surface must therefore have positive curvature. (You should fill in the details for this argument).
Jan
27
comment Does there exist a surface homemomorphic to a torus with positive Gaussian curvature?
@Felipe: no (deform a little bit the tip of a sphere for example), but the Euler characteristic is. Therein lies the power of Gauss-Bonnet! It combines topological data (Euler characteristic) with geometrical data (global curvature).
Jan
26
comment How to introduce category theory to a high school audience?
I agree with what Martin said. The first examples that come to mind are lcm/gcd of integers and sup/inf of real numbers. There are many other elementary examples like these.
Jan
23
revised Verification of my solution of $xy'=2y$
changed undescriptive title
Jan
18
awarded  Nice Question
Jan
18
reviewed Approve magical isoceles triangle and 13/15 ratio
Jan
18
reviewed Approve Show a module is simple
Jan
9
comment Stopping the “Will I need this for the test” question
This is as depressing as it is true.
Dec
30
revised When are generalized Severi-Brauer varieties trivial?
I mistook dimension for -reduced dimension-. Also, added link to the MO counterpart
Dec
28
reviewed Reject Solving $\phi(n)=22$
Dec
27
reviewed Edit What is the benefit of the theory of categories?
Dec
27
revised What is the benefit of the theory of categories?
edited some typos
Dec
27
revised When are generalized Severi-Brauer varieties trivial?
edited tags
Dec
27
awarded  Custodian
Dec
27
reviewed Approve Integral of $\frac{1}{x^4+1}$
Dec
26
revised When are generalized Severi-Brauer varieties trivial?
edited tags
Dec
26
comment A group of order 561 is cyclic.
I don't understand how this question has 6 upvotes (as of now).
Dec
26
asked When are generalized Severi-Brauer varieties trivial?
Dec
10
awarded  Popular Question