Pague parcelado visa master hipercard com MercadoPago. Por favor, tente novamente. Quantidade: Adicionar ao carrinho. Coherent homotopy over a fixed space K.

## PMH1 Algebraic Topology

Hardie, K. Modern foundations for stable homotopy theory A. Elmendorf et al.. Completions in algebra and topology J. Greenlees, J. Equivariant stable homotopy theory J.

## Handbook of Algebraic Topology : I. M. James :

The stable homotopy theory of finite complexes D. The EHP sequence and periodic homotopy M. Mahowald, R. Introduction to nonconnective Im J -theory M.

Crabb, K. Applications of nonconnective Im J -theory K.

Stable homotopy and iterated loop spaces G. Carlsson, R. Stable operations in generalized cohomology J.

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- MA3H6 Algebraic Topology.
- Top Authors.
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Unstable operations in generalized cohomology J. Boardman et al. Differential graded algebras in topology Y.

## MA3H6 Algebraic Topology

MATH Algebraic Topology IV The basic method of algebraic topology is to assign an algebraic system say, a group or a ring to each topological space in such a way that homeomorphic spaces have isomorphic systems. Outline of Course Aim: The module will provide a deeper knowledge in the field of topology a balanced introduction having been provided in Topology III.

Term 1 Homotopy properties of cell complexes: Cell complexes, main constructions mapping cones and cylinders, products , examples.

Elements of homological algebra: Chain complexes, homology, chain homotopy, exact sequences, Euler characteristic. Homology theory of topological spaces: Singular homology of topological spaces, homotopy invariance, Mayer-Vietoris sequences, relation between homology and the fundamental group, geometric interpretation of homology classes, homology groups of cell complexes.

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Applications: Brouwer fixed point theorem, Jordan curve theorem, invariance of domain. Applications: Alexander duality, non-embeddability of non-orientable closed surface in Euclidean 3-space.