Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polytope Novikov Homology   Let $M$ be a closed manifold and $\mathcal{A} \subseteq H^1_{\mathrm{dR}}(M)$
a polytope. For each $a \in \mathcal{A}$ we define a Novikov chain complex with
a multiple finiteness condition encoded by the polytope $\mathcal{A}$. The
resulting polytope Novikov homology generalizes the ordinary Novikov homology.
We prove that any two cohomology classes in a prescribed polytope give rise to
chain homotopy equivalent polytope Novikov complexes over a Novikov ring
associated to said polytope. As applications we present a novel approach to the
(twisted) Novikov Morse Homology Theorem and prove a new polytope Novikov
Principle. The latter generalizes the ordinary Novikov Principle and a recent
result of Pajitnov in the abelian case.

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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: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: physics