The set of all such classes can be given an algebraic structure called a group, the fundamental group of the region, whose structure varies according to the type of region.
Then the genus of (C'_t) grows by 1, and the monodromy is trivial on the meridian (alpha ) (image of the generator of the fundamental group of the cylinder we are attaching).
We refer to this setting as the orthogonal case, since the fundamental group leaving the Dirac operator ∂ X ̲ invariant is the special orthogonal group SO ( 2 n, R ), which is doubly covered by the Spin ( m ) group of the Clifford algebra Cl ( V 2 n, 0 ).
The fundamental group leaving the Dirac operator invariant is the special orthogonal group, doubly covered by the spin group of the Clifford algebra.
L. Ji, K. Murty, L. Saper, and J. Scherk, The Congruence Subgroup Kernel and the Fundamental Group of the Reductive Borel-Serre Compactification (June, 2011).
These results are obtained by studying the asymptotic distribution of the lattice in hyperbolic space generated by the fundamental group of the covering surface.
Since R is the fundamental group of the Cayley graph of H, whose vertices corresponding to the elements of begin{aligned} H = left{ x^i y^j | 0 le i le n-1, 0 le j le m-1 right}, end{aligned}and R is a free group on (mn+1) generators.
Now you will want to get theorems of the following sorts: if X can be continuously deformed into another space Y, then their fundamental groups are isomorphic; the fundamental group of a product is the product of the fundamental groups; etc.
(1) It is interesting to observe that one can view the orbifold fundamental group, in the case of curves, as the quotient of a bona fide fundamental group.
