Download Algebraic Topology, Homotopy and Homology by R. Switzer PDF

By R. Switzer

Show description

Read Online or Download Algebraic Topology, Homotopy and Homology PDF

Best topology books

Art Meets Mathematics in the Fourth Dimension (2nd Edition)

To work out items that stay within the fourth size we people would have to upload a fourth measurement to our third-dimensional imaginative and prescient. An instance of such an item that lives within the fourth measurement is a hyper-sphere or “3-sphere. ” the hunt to visualize the elusive 3-sphere has deep historic roots: medieval poet Dante Alighieri used a 3-sphere to show his allegorical imaginative and prescient of the Christian afterlife in his Divine Comedy.

Algebraic L-theory and topological manifolds

This publication provides the definitive account of the functions of this algebra to the surgical procedure type of topological manifolds. The imperative result's the id of a manifold constitution within the homotopy kind of a Poincaré duality house with an area quadratic constitution within the chain homotopy kind of the common conceal.

Differential Forms in Algebraic Topology

The guideline during this publication is to take advantage of differential kinds as an reduction in exploring many of the much less digestible elements of algebraic topology. Accord­ ingly, we circulation basically within the realm of gentle manifolds and use the de Rham conception as a prototype of all of cohomology. For purposes to homotopy conception we additionally talk about in terms of analogy cohomology with arbitrary coefficients.

Extra resources for Algebraic Topology, Homotopy and Homology

Example text

G. two finite groups with the same number of conjugacy classes, hence the same number of isomorphism classes of irreducible representations). We obtain a more geometric notion of Morita equivalence for groups by considering actions on manifolds rather than on linear spaces. e. manifolds where G acts on the left, H acts on the right, and the actions commute. The “tensor product” of such bimodules is defined by the orbit space G XH ∗ H YK := X × Y/H, where H acts on X × Y by (x, y) → (xh, h−1 y). The result of this operation may no longer be smooth, even if X and Y are.

This can also be described as an infinite-dimensional symplectic reduction. The resulting space is a groupoid but may not be a manifold. When it is a manifold, it is the source-simply-connected symplectic groupoid of P . When G(P ) is not a manifold, as the leaf space of a foliation, it can be considered as a differentiable stack, and even as a symplectic stack. 2 Symplectic groupoids 43 groupoid; we will call it an S-groupoid. The first steps of this program have been carried out by Tseng and Zhu [83].

If one is given two left modules (one could do the same for right modules, of course), one can apply the tensor product construction by changing the “handedness” of one of them. Thus, if S and S are left P modules, then S is a right module, and we can form the tensor product S ∗ S. We call this the classical intertwiner space [95, 96] of S and S and denote it by Hom(S, S ). The name and notation come from the case of modules over an algebra, where the tensor product Y∗ ⊗ X is naturally isomorphic to the space of module homomorphisms from Y to X when these modules are “finite dimensional”.

Download PDF sample

Rated 4.56 of 5 – based on 10 votes