Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The topological modular forms of $\mathbb{R}P^2$ and $\mathbb{R}P^2
  \wedge \mathbb{C}P^2$   In this paper, we study the elliptic spectral sequence computing
$tmf_*(\mathbb{R} P^2)$ and $tmf_* (\mathbb{R} P^2 \wedge \mathbb{C} P^2)$.
Specifically, we compute all differentials and resolve exotic extensions by 2,
$\eta$, and $\nu$. For $tmf_* (\mathbb{R} P^2 \wedge \mathbb{C} P^2)$, we also
compute the effect of the $v_1$-self maps of $\mathbb{R} P^2 \wedge \mathbb{C}
P^2$ on $tmf$-homology.

28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph