Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Aspherical Relative Presentations All Over Again   The concept of asphericity for relative group presentations was introduced
twenty five years ago. Since then, the subject has advanced and detailed
asphericity classifications have been obtained for various families of
one-relator relative presentations. Through this work the definition of
asphericity has evolved and new applications have emerged.
  In this article we bring together key results on relative asphericity, update
them, and exhibit them under a single set of definitions and terminology. We
describe consequences of asphericity and present techniques for proving
asphericity and for proving non-asphericity. We give a detailed survey of
results concerning one-relator relative presentations where the relator has
free product length four.

5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th