# A Concise Course in Algebraic Topology (Chicago Lectures in by J. P. May

By J. P. May

J. Peter May's technique displays the big inner advancements inside of algebraic topology during the last numerous many years, such a lot of that are principally unknown to mathematicians in different fields. yet he additionally keeps the classical shows of assorted themes the place acceptable. so much chapters finish with difficulties that additional discover and refine the suggestions awarded. the ultimate 4 chapters supply sketches of considerable parts of algebraic topology which are as a rule passed over from introductory texts, and the publication concludes with an inventory of recommended readings for these drawn to delving additional into the field.

**Read or Download A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series) PDF**

**Best algebraic geometry books**

**Bioceramics: Properties, Characterizations, and Applications**

Bioceramics: houses, Characterization, and functions could be a normal creation to the makes use of of ceramics and glasses within the human physique for the needs of supporting, therapeutic, correcting deformities, and restoring misplaced functionality. With over 30 years adventure, the writer constructed the textual content as an outgrowth of an undergraduate direction for senior scholars in biomedical engineering and should emphasize the basics and functions in smooth implant fabrication, and also will care for tissue engineering scaffolds made up of ceramics.

**An Introduction to Algebraic Geometry and Algebraic Groups (Oxford Graduate Texts in Mathematics)**

An available textual content introducing algebraic geometries and algebraic teams at complicated undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the speculation of affine algebraic teams from first ideas. construction at the historical past fabric from algebraic geometry and algebraic teams, the textual content presents an advent to extra complex and specialized fabric.

- Complex Algebraic Geometry
- Geometry of Foliations, 1st Edition
- Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics)
- Geometry and Topology of Configuration Spaces

**Additional resources for A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series)**

**Example text**

Let Cov(B) denote the category of coverings of the space B; when B is understood, we write Cov(E, E ′ ) for the set of maps E −→ E ′ of coverings of B. 7. THE CLASSIFICATION OF COVERINGS OF SPACES 29 Lemma. A map g : E −→ E ′ of coverings is itself a covering. Proof. The map g is surjective by the algebraic analogue. The fundamental neighborhoods for g are the components of the inverse images in E ′ of the neighborhoods of B which are fundamental for both p and p′ . The following remarkable theorem is an immediate consequence of the fundamental theorem of covering space theory.

If i : Y −→ M f is the inclusion, then r ◦ i = id and id ≃ i ◦ r. In fact, we can define a deformation h : M f × I −→ M f of M f onto i(Y ) by setting h(y, t) = y and h((x, s), t) = (x, (1 − t)s). It is not hard to check directly that j : X −→ M f satisfies the HEP, and this will also follow from the general criterion for a map to be a cofibration to which we turn next. 4. A criterion for a map to be a cofibration We want a criterion that allows us to recognize cofibrations when we see them. We shall often consider pairs (X, A) consisting of a space X and a subspace A.

Then k −→ t(k) specifies an isomorphism between K and the group Aut(H). Let X and Y be connected, locally path connected, and Hausdorff. A map f : X −→ Y is said to be a local homeomorphism if every point of X has an open neighborhood that maps homeomorphically onto an open set in Y . 3. Give an example of a surjective local homeomorphism that is not a covering. 4. * Let f : X −→ Y be a local homeomorphism, where X is compact. ) covering with finite fibers. Let X be a G-space, where G is a (discrete) group.