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<!--* !!! To do: determine which 1-connected 5-manifolds appear as Brieskorn varieties. --> Given a finitely generated abelian group $G$, let $X_G$ denote the degree 2 Moore space with $H_2(X_G) = G$.

...heres. [[Wikipedia:Connected_sum|Connected sum]] makes $\Theta_n$ into an abelian group with inverse given by reversing orientation. An important subgroup o ...ct exotic spheres. We review four such constructions: plumbing, Brieskorn varieties, sphere-bundles and twisting.

is an Abelian group with respect to the disjoint union. This group ...es are algebraic, but one also needs to represent $-[H_{ij}]$ by algebraic varieties!)

*this includes, in particular, the case of trivial, Abelian, solvable, and nilpotent fundamental groups. * The Lipschitz simplicial volume of Hilbert modular varieties coincides with the simplicial volume {{cite|Löh&Sauer2009a}}.

... of finite cyclic groups on [[Exotic_spheres#Brieskorn_varieties|Brieskorn varieties]]. See the [[Fake lens spaces#Construction and examples|constructions and ... $\bar \Sigma_N (d) \subset {\mathbb Q} R^{(-1)^d}_{\widehat G}$ is a free abelian group. If $N$ is odd then its rank is $(N-1)/2$. If $N$ is even then its ra

The middle homology group $H_n(F_{\theta})$ is a free abelian group of rank $\mu$. A symmetric or skew symmetric bilinear form on a free abelian group is usually referred to as a lattice. $s$ is called the '''Milnor latt

* [[Abelian varieties]] * [[Exotic spheres#Brieskorn varieties|Brieskorn spheres]]