Notes $\def\Z{\mathbb Z} \def\Q{\mathbb Q} \def\Torelli{\mathcal I}$

These are some miscellaneous notes I have written. They are not intended for publication and for the most part do not contain original material.

[pdf] [abstract] One-relator groups

[pdf] [abstract] A quick proof of the Seifert-Van Kampen theorem

[pdf] [abstract] The isoperimetric inequality in the plane

[pdf] [abstract] The generalized Schoenflies theorem

[pdf] [abstract] Homotopy groups of spheres and low-dimensional topology

[pdf] [abstract] The complex of cycles on a surface (after Bestvina-Bux-Margalit)

[pdf] [abstract] The Torelli group and congruence subgroups of the mapping class group

[pdf] [abstract] Rochlin's theorem on signatures of spin 4-manifolds via algebraic topology

[pdf] [abstract] The congruence subgroup problem for SLn($\Z$)

[pdf] [abstract] The fundamental theorem of projective geometry

[pdf] [abstract] The Borel density theorem

[pdf] [abstract] The action on homology of finite groups of automorphisms of surfaces and graphs

[pdf] [abstract] A categorical construction of free groups

[pdf] [abstract] A quick proof of the classification of surfaces

[pdf] [abstract] The abelianization of the level L mapping class group