Topics in topology: The signature theorem and some of its applications
by Liviu I. Nicolaescu
Publisher: University of Notre Dame 2008
Number of pages: 159
The author discusses several exciting topological developments that took place during the fifties decade which radically changed the way we think about many issues. Topics covered: Poincare duality, Thom isomorphism, Euler, Chern and Pontryagin classes, cobordisms groups, signature formula.
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by D. G. Bourgin - Macmillan
Contents: Preliminary algebraic background; Chain relationships; The absolute homology groups and basic examples; Relative omology modules; Manifolds and fixed cells; Omology exact sequences; Simplicial methods and inverse and direct limits; etc.
by Boris Dubrovin - arXiv
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Topics: WDVV equations and Frobenius manifolds; Polynomial solutions of WDVV; Symmetries of WDVV; etc.
by Daniel Dugger - University of Oregon
This is an expository paper on homotopy colimits and homotopy limits. These are constructions which should arguably be in the toolkit of every modern algebraic topologist. Many proofs are avoided, or perhaps just sketched.
by Dikran Dikranjan - UCM
These notes provide a brief introduction to topological groups with a special emphasis on Pontryaginvan Kampen's duality theorem for locally compact abelian groups. We give a completely self-contained elementary proof of the theorem.