Geometry of Infinitely Presented Small Cancellation Groups and Quasi-homomorphisms

We study the geometry of infinitely presented groups satisfying the small cancellation condition $C^{\prime }(1/8)$ , and introduce a standard decomposition (called the criss-cross decomposition ) for the elements of such groups. Our method yields a direct construction of a linearly independent set of power continuum in the kernel of the comparison map between the bounded and the usual group cohomology in degree 2, without the use of free subgroups and extensions.