Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy complex projective spaces with Pin(2)-action   Let $M$ be a manifold homotopy equivalent to the complex projective space $\C
P^m$. Petrie conjectured that $M$ has standard total Pontrjagin class if $M$
admits a non-trivial action by $S^1$. We prove the conjecture for $m<12$ under
the assumption that the action extends to a nice $Pin(2)$-action with fixed
point. The proof involves equivariant index theory for $Spin^c$-manifolds and
Jacobi functions as well as classical results from the theory of transformation
groups.

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The categories of this paper are: econ
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The categories of this paper are: stat
12
The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga