Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euler characteristics of generalized Haken manifolds   Haken n-manifolds have been defined and studied by B. Foozwell and H.
Rubinstein in analogy with the classical Haken manifolds of dimension 3, based
upon the the theory of boundary patterns developed by K. Johannson. The Euler
characteristic of a Haken manifold is analyzed and shown to be equal to the sum
of the Charney-Davis invariants of the duals of the boundary complexes of the
n-cells at the end of a hierarchy. These dual complexes are shown to be flag
complexes. It follows that the Charney-Davis Conjecture is equivalent to the
Euler Characteristic Sign Conjecture for Haken manifolds. Since the
Charney-Davis invariant of a flag simplicial 3-sphere is known to be
non-negative it follows that a closed Haken 4-manifold has non-negative Euler
characteristic. These results hold as well for generalized Haken manifolds
whose hierarchies can end with compact contractible manifolds rather than
cells.

18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-lat