A generalization of Stokes theorem on combinatorial manifolds

Abstract

For an integer $m\ge 1$, a combinatorial manifold $\tilde{M}$ is defined to be a geometrical object $\tilde{M}$ such that for $\forall p\in \tilde{M}$, there is a local chart $(U_p,{\varphi }_p)$ enable ${\varphi }_p:U_p\to B^{n_{i_1}}\bigcup B^{n_{i_2}}\bigcup ...\bigcup B^{n_{i_{s(p)}}}$ with $B^{n_{i_1}}\bigcap B^{n_{i_2}}\bigcap ...\bigcap B^{n_{i_{s(p)}}}\ne \varnothing$, where $B^{n_{i_j}}$ is an $n_{i_j}$-ball for integers $1\le j\le s(p)\le m$. Integral theory on these smoothly combinatorial manifolds are introduced. Some classical results, such as those of {\it Stokes'} theorem and {\it Gauss'} theorem are generalized to smoothly combinatorial manifolds in this paper.

17 pages

References in corpus (1)

• Combinatorial Speculations and the Combinatorial Conjecture for Mathematics