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Results tagged with curves-and-surfaces
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user 20516
A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line
2
votes
Syzygies in Steinberg module of genus 2 mapping class group $\mathrm{MCG}(\Sigma_2)$
I recently returned to this question, and have found a formal solution to Closing the Steinberg symbol in genus two using Mark C. Bell's wonderful curver program.
In low genus it was expected that an …
- 2,274
7
votes
1
answer
198
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Syzygies in Steinberg module of genus 2 mapping class group $\mathrm{MCG}(\Sigma_2)$
$\DeclareMathOperator\MCG{MCG}$Consider the mapping class group $\MCG(\Sigma_2)$ of the closed genus 2 oriented surface $\Sigma_2$. The algebraic-duality theory of $\MCG_2:=\MCG(\Sigma_2)$ is explicit …
- 2,274
0
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When is the cut locus a finite tree?
Edited Jan31, 2022: the cut locus of the curve $\gamma$ is a finite tree if the boundary is smooth and if the curve bounds a contractible domain, i.e. $\Omega \approx \{pt\}$. This follows from Blum's …
- 2,274