Editing Algebraic topology (section)

==References==
{{Commons category|Algebraic topology}}
{{Wikiquote}}
*{{citation |first=Dylan G. L. |last=Allegretti |url=http://www.math.uchicago.edu/~may/VIGRE/VIGREREU2008.html |title=Simplicial Sets and van Kampen's Theorem |year=2008}} ''(Discusses generalized versions of van Kampen's theorem applied to topological spaces and simplicial sets).''
*{{citation |last=Bredon |first=Glen E. |author-link=Glen Bredon|title=Topology and Geometry |year=1993 |publisher=Springer |series=Graduate Texts in Mathematics |volume=139 |url=https://books.google.com/books?id=G74V6UzL_PUC |isbn=0-387-97926-3}}.
*{{citation |first=R. |last=Brown |author-link=Ronald Brown (mathematician) |url=http://www.bangor.ac.uk/r.brown/hdaweb2.html |title=Higher dimensional group theory |year=2007 |access-date=2022-08-17 |archive-date=2016-05-14 |archive-url=http://arquivo.pt/wayback/20160514115207/http://www.bangor.ac.uk/r.brown/hdaweb2.html |url-status=dead }} ''(Gives a broad view of higher-dimensional van Kampen theorems involving multiple groupoids)''.
*{{citation |first1=R. |last1=Brown |first2=A. |last2=Razak |title=A van Kampen theorem for unions of non-connected spaces |journal=Arch. Math. |volume=42 |pages=85–88 |year=1984 |doi=10.1007/BF01198133 |s2cid=122228464 }}. "Gives a general theorem on the [[fundamental groupoid]] with a set of base points of a space which is the union of open sets."
*{{citation |first1=R. |last1=Brown |first2=K. |last2=Hardie |first3=H. |last3=Kamps |first4=T. |last4=Porter |title=The homotopy double groupoid of a Hausdorff space |journal=Theory Appl. Categories |volume=10 |issue=2 |pages=71–93 |year=2002 |url=http://www.emis.de/journals/TAC/volumes/10/2/10-02abs.html}}.
*{{citation |first1=R. |last1=Brown |first2=P.J. |last2=Higgins |title=On the connection between the second relative homotopy groups of some related spaces |journal=Proc. London Math. Soc. |volume=S3-36 |issue= 2|pages=193–212 |year=1978 |doi=10.1112/plms/s3-36.2.193 }}. "The first 2-dimensional version of van Kampen's theorem." 
*{{citation |first1=Ronald |last1=Brown |first2=Philip J. |last2=Higgins |first3=Rafael |last3=Sivera |title=Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids |url=http://www.bangor.ac.uk/~mas010/nonab-a-t.html |year=2011 |publisher=European Mathematical Society |isbn=978-3-03719-083-8 |series=European Mathematical Society Tracts in Mathematics |volume=15|archive-url=https://web.archive.org/web/20090604050453/http://www.bangor.ac.uk/~mas010/nonab-a-t.html |archive-date=2009-06-04 |arxiv=math/0407275 }} This provides a homotopy theoretic approach to basic algebraic topology, without needing a basis in [[singular homology]], or the method of simplicial approximation. It contains a lot of material on [[crossed module]]s.
* {{ citation | first1 = John B. | last1 = Fraleigh | year = 1976 | isbn = 0-201-01984-1 | title = A First Course In Abstract Algebra | edition = 2nd | publisher = [[Addison-Wesley]] | location = Reading }}
*{{citation |author-link1=Marvin Greenberg |last1=Greenberg |first1=Marvin J. |first2=John R. |last2=Harper |title=Algebraic Topology: A First Course, Revised edition |year=1981 |publisher=Westview/Perseus |series=Mathematics Lecture Note Series |isbn=9780805335576 |url-access=registration |url=https://archive.org/details/algebraictopolog00gree_0 }}. A functorial, algebraic approach originally by Greenberg with geometric flavoring added by Harper. 
*{{citation| last=Hatcher |first= Allen |author-link=Allen Hatcher| title=Algebraic Topology |url=http://pi.math.cornell.edu/~hatcher/AT/ATpage.html |year= 2002 |publisher=Cambridge University Press |place=Cambridge |isbn=0-521-79540-0}}. A modern, geometrically flavoured introduction to algebraic topology.
*{{citation |first=Philip J. |last=Higgins |title=Notes on categories and groupoids |url=https://books.google.com/books?id=IqdIAAAAMAAJ |year=1971 |publisher=Van Nostrand Reinhold |isbn=9780442034061}}
*{{citation| last=Maunder |first=C. R. F. |title=Algebraic Topology |journal=Nature |year=1970 |volume=227 |issue=5259 |page=756 |publisher= Van Nostrand Reinhold |doi=10.1038/227756a0 |bibcode=1970Natur.227..756F |place=London |isbn=0-486-69131-4}}.
*{{citation |author-link=Tammo tom Dieck |first=Tammo |last=tom Dieck |title=Algebraic Topology |url=https://books.google.com/books?id=ruSqmB7LWOcC |year=2008 |publisher=European Mathematical Society |isbn=978-3-03719-048-7 |series=EMS Textbooks in Mathematics}}
* {{citation|first=Egbert|last= van Kampen|author-link=Egbert van Kampen| title=On the connection between the fundamental groups of some related spaces| journal=[[American Journal of Mathematics]]|volume= 55 |year=1933 |issue= 1|pages=261–7 |jstor=51000091}}