Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third homology of SL_2 and the indecomposable K_3   It is known that, for an infinite field F, the indecomposable part of K_3(F)
and the third homology of SL_2(F) are closely related. In fact, there is a
canonical map \alpha: H_3(SL_2(F),Z)_F* --> K_3(F)^ind. Suslin has raised the
question that, is \alpha an isomorphism? Recently Hutchinson and Tao have shown
that this map is surjective. They also gave some arguments about its
injectivity. In this article, we improve their arguments and show that \alpha
is bijective if and only if the natural maps H_3(GL_2(F), Z)--> H_3(GL_3(F), Z)
and H_3(SL_2(F), Z)_F* --> H_3(GL_2(F), Z) are injective.

35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin