Lectures on Sheaf Theory
by C.H. Dowker
Publisher: Tata Institute of Fundamental Research 1957
Number of pages: 201
A sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. Contents: Sheaves; Sections; Cohomology groups of a space with coefficients in a presheaf; Introduction of the family Phi; Singular chains; Direct sum of modules; etc.
Download or read it online for free here:
by John Douglas Moore - Springer
A streamlined introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure.
by Curtis T. McMullen - Harvard University
Contents: Introduction; Background in set theory; Topology; Connected spaces; Compact spaces; Metric spaces; Normal spaces; Algebraic topology and homotopy theory; Categories and paths; Path lifting and covering spaces; Global topology; etc.
by David Ellwood, at al. - American Mathematical Society
Mathematical gauge theory studies connections on principal bundles. The book provides an introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds.
by Neil Lambert - King's College London
From the table of contents: Manifolds (Elementary Topology and Definitions); The Tangent Space; Maps Between Manifolds; Vector Fields; Tensors; Differential Forms; Connections, Curvature and Metrics; Riemannian Manifolds.