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An Introduction to Algebraic Topology (1988), Springer-Verlag; ISBN 0-387-96678-1 An Introduction to the Theory of Groups (1995), Springer-Verlag; ISBN 0-387-94285-8 A First Course in Abstract Algebra (2000), Prentice Hall; ISBN 0-13-011584-3
110 Differential Algebraic Topology: From Stratifolds to Exotic Spheres, Matthias Kreck (2010, ISBN 978-0-8218-4898-2) 111 Ricci Flow and the Sphere Theorem, Simon Brendle (2010, ISBN 978-0-8218-4938-5) 112 Optimal Control of Partial Differential Equations: Theory, Methods and Applications, Fredi Troltzsch (2010, ISBN 978-0-8218-4904-0)
A torus, one of the most frequently studied objects in algebraic topology. Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
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He was known for his book on non-Euclidean geometry (1st edition, 1974; 4th edition, 2008) [3] [4] and his book on algebraic topology (1st edition, 1967, published with the title Lectures on Algebraic Topology; revised edition published, with John R. Harper as co-author, in 1981 with the title Algebraic Topology: A First Course). [5] [6] [7]
In algebraic topology and algebraic geometry, a cyclic cover or cyclic covering is a covering space for which the set of covering transformations forms a cyclic group. [1] [2] As with cyclic groups, there may be both finite and infinite cyclic covers.
The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and ...
Differential graded algebra: the algebraic structure arising on the cochain level for the cup product; Poincaré duality: swaps some of these; Intersection theory: for a similar theory in algebraic geometry