By Anant R. Shastri
Building on rudimentary wisdom of genuine research, point-set topology, and easy algebra, Basic Algebraic Topology presents lots of fabric for a two-semester path in algebraic topology.
The publication first introduces the required basic thoughts, corresponding to relative homotopy, fibrations and cofibrations, type thought, cellphone complexes, and simplicial complexes. It then specializes in the elemental team, overlaying areas and undemanding facets of homology idea. It offers the primary gadgets of research in topology visualization: manifolds. After constructing the homology concept with coefficients, homology of the goods, and cohomology algebra, the publication returns to the learn of manifolds, discussing Poincaré duality and the De Rham theorem. a short advent to cohomology of sheaves and Čech cohomology follows. The center of the textual content covers larger homotopy teams, Hurewicz’s isomorphism theorem, obstruction idea, Eilenberg-Mac Lane areas, and Moore-Postnikov decomposition. the writer then relates the homology of the complete area of a fibration to that of the bottom and the fiber, with functions to attribute sessions and vector bundles. The booklet concludes with the elemental concept of spectral sequences and several other purposes, together with Serre’s seminal paintings on larger homotopy groups.
Thoroughly classroom-tested, this self-contained textual content takes scholars all of the method to changing into algebraic topologists. historic comments during the textual content make the topic extra significant to scholars. additionally compatible for researchers, the ebook offers references for additional interpreting, provides complete proofs of all effects, and contains quite a few workouts of various levels.
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Extra resources for Basic Algebraic Topology
Basic Algebraic Topology by Anant R. Shastri