Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The homotopy groups of a homotopy group completion   Let $M$ be a topological monoid with homotopy group completion $\Omega BM$.
Under a strong homotopy commutativity hypothesis on $M$, we show that $\pi_k
(\Omega BM)$ is the quotient of the monoid of free homotopy classes $[S^k, M]$
by its submonoid of nullhomotopic maps.
  We give two applications. First, this result gives a concrete description of
the Lawson homology of a complex projective variety in terms of point-wise
addition of spherical families of effective algebraic cycles. Second, we apply
this result to monoids built from the unitary, or general linear,
representation spaces of discrete groups, leading to results about lifting
continuous families of characters to continuous families of representations.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th