Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morita's trace maps on the group of homology cobordisms   Morita introduced in 2008 a 1-cocycle on the group of homology cobordisms of
surfaces with values in an infinite-dimensional vector space. His 1-cocycle
contains all the "traces" of Johnson homomorphisms which he introduced fifteen
years earlier in his study of the mapping class group. In this paper, we
propose a new version of Morita's 1-cocycle based on a simple and explicit
construction. Our 1-cocycle is proved to satisfy several fundamental
properties, including a connection with the Magnus representation and the LMO
homomorphism. As an application, we show that the rational abelianization of
the group of homology cobordisms is non-trivial. Besides, we apply some of our
algebraic methods to compare two natural filtrations on the automorphism group
of a finitely-generated free group.

21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph