Geometric formulation of the covariant phase space methods with boundaries

We analyze in full-detail the geometric structure of covariant phase space (CPS) any local field theory defined over a space-time with boundary. To this end, we introduce new frame: "relative bicomplex framework". It is result merging an extended version framework" (initially developed context algebraic topology by R.~Bott and L.W.~Tu 1980s to deal boundaries) variational framework (the differential arena for calculus). The relative natural one theories boundary contributions, including corner contributions. In fact, prove formal equivalence between non-relative same no With these tools at hand, endow solutions (pre)symplectic canonically associated action which, general, has also study symmetries construct, large group them, their Noether currents, charges. Moreover, completely characterize arbitrariness (or lack thereof fiber bundles contractible fibers) constructions. This clarifies many misconceptions about role terms CPS description theory. Finally, provide what call CPS-algorithm construct aforementioned apply it some relevant examples.