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His work is closely linked with the emergence of algebraic topology;
Spanier returned to algebraic topology for the publications in the last years of his life.
He changed supervisors andbegan working on algebraic topology with Shaun Wylie.
Algebraic topology underwent a spectacular development in the years following the second world war.
A solution to these problems required the development of a new kind of algebraic topology.
After this he worked in algebraic topology, and in 1932 he called for the unification of the two areas.
In the 1950s Milnor did a substantial amount of work on algebraic topology which is discussed in.
Most of Hopf's work was in algebraic topology where he can be thought of as continuing Brouwer's work.
His aim was to bring together point-set topology and algebraic topology with his 1932 paper.
We have suggested that his work on algebraic topology went on until around the time that his famous book was published in 1966.
It should not be confused with combinatorial topology which is an older name for algebraic topology.
This latter work is an introduction to algebraic topology for a reader without background in general topology. .
Mathematician of penetration and originality,whose inventions revolutionized partial differential equations and algebraic topology.
Particularly, he reported on applications to noncommutative algebraic topology, noncommutative integration and noncommutative dynamical systems.
In the course of his work he introduced many of what would be considered today the basic tools of algebraic topology.
After his 1934 paper with Schauder,Leray published a paper on algebraic topology in the following year on the topology of Banach spaces.
However, he was most strongly influenced by Henry Whitehead,who led the foremost British school of algebraic topology.
The third volume of collected papers by Raoul Bott represents his works on the algebraic topology aspects of foliations and Gelfand-Fuchs cohomology.
Even today the Poincaré conjecture remains as one of the most baffling andchallenging unsolved problems in algebraic topology.
His main interests were in algebraic topology and, in the autumn of 1982, he went to the University of California at Berkeley to continue his research.
After his release in 1945 Leray published a three part work Algebraic topology taught in captivity.
This counter-example sent Poincaré back to the drawing board andthereby contributed to a clarification of some basic notions of algebraic topology.
Serre's theorem led to rapid progress not only in homotopy theory but in algebraic topology and homological algebra in general.
It is in two parts,the first contains a description of the topics that Adams thought essential for any young mathematician interested in algebraic topology.
His methods allowed arguments of combinatorial and algebraic topology to be applied to point set topology and brought together these areas.
He published the book Geometric integration theory In 1957 which describes his work on the interactions between algebraic topology and the theory of integration.
The exposition of the book is aimed at the reader who has some understanding of algebraic topology and would like to understand the aspects of the theory of compact Lie groups that are relevant to algebraic topology. .
He conjectured results about the number of solutions to polynomial equations over the integers using intuition on how algebraic topology should apply in this novel situation.
It was characteristic of Hopf 's views on our science that this meant not only learning algebraic topology- then a very young field- but also getting acquainted with group theory, differential geometry, and algebra in the"abstract" sense of the Emmy Noether school.
Another text which would have a huge influence on the development of the field was Algebraic topology which was published in 1942.