Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrical Theory on Combinatorial Manifolds   For an integer $m\geq 1$, a combinatorial manifold $\widetilde{M}$ is defined
to be a geometrical object $\widetilde{M}$ such that for $\forall
p\in\widetilde{M}$, there is a local chart $(U_p,\phi_p)$ enable $\phi_p:U_p\to
B^{n_{i_1}}\bigcup B^{n_{i_2}}\bigcup...\bigcup B^{n_{i_{s(p)}}}$ with
$B^{n_{i_1}}\bigcap B^{n_{i_2}}\bigcap...\bigcap
B^{n_{i_{s(p)}}}\not=\emptyset$, where $B^{n_{i_j}}$ is an $n_{i_j}$-ball for
integers $1\leq j\leq s(p)\leq m$. Topological and differential structures such
as those of $d$-pathwise connected, homotopy classes, fundamental $d$-groups in
topology and tangent vector fields, tensor fields, connections, {\it Minkowski}
norms in differential geometry on these finitely combinatorial manifolds are
introduced. Some classical results are generalized to finitely combinatorial
manifolds. Euler-Poincare characteristic is discussed and geometrical
inclusions in Smarandache geometries for various geometries are also presented
by the geometrical theory on finitely combinatorial manifolds in this paper.

21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex