Serrurier Marseille E-books > Topology > Algebraic Topology, Homotopy and Homology - download pdf or read online

Algebraic Topology, Homotopy and Homology - download pdf or read online

By R. Switzer

Show description

Read Online or Download Algebraic Topology, Homotopy and Homology PDF

Best topology books

New PDF release: Open Problems in Topology

This quantity grew from a dialogue by means of the editors at the trouble of discovering stable thesis difficulties for graduate scholars in topology. even if at any given time we each one had our personal favourite difficulties, we said the necessity to supply scholars a much broader choice from which to settle on an issue ordinary to their pursuits.

Download e-book for kindle: A Course in Point Set Topology by John B. Conway

This textbook in aspect set topology is aimed toward an upper-undergraduate viewers. Its mild speed might be necessary to scholars who're nonetheless studying to put in writing proofs. necessities comprise calculus and not less than one semester of study, the place the scholar has been appropriately uncovered to the tips of simple set thought comparable to subsets, unions, intersections, and features, in addition to convergence and different topological notions within the actual line.

Additional resources for Algebraic Topology, Homotopy and Homology

Sample text

Regular Surface 23 chart X(s1 , s2 ) = (s1 , s2 , 0)T , where (s1 , s2 )T ∈ (0, 1) × (0, 1), has a boundary. Indeed, ∂ S = [{0} × (0, 1)] ∪ [{1} × (0, 1)] ∪ [(0, 1) × {0}] ∪ [(0, 1) × {1}] . A closed surface is a surface that is compact and without boundary. 20) for some constant c. If G is at least C 1 in a neighborhood ⊂ 3 of some point in Γ , and ∂i G = 0 in (for some fixed i = 1, 2, 3), then one can use the implicit function theorem to solve for one of the variables x1 , x2 , x3 . For example, if ∂3 G = 0, then there exists an open set U and an F : U → such that x3 = F (x1 , x2 ), where (x1 , x2 , x3 )T ∈ ∩Γ.

Thus, we say, the plane 2 is orientable. In fact, any plane is orientable, with orientation determined by selecting one of the two normal 40 Chapter 3. 2. Illustration of orientability (arrows depict unit normal vector ν). (a) The unit sphere can be covered with a differentiable unit normal vector field (here a positive orientation is chosen). (b) The Möbius strip is a nonorientable surface. It is not possible to choose a normal vector field that is differentiable (or even continuous) over the entire surface.

51) with respect to q (while keeping s fixed). Because kn (s, q) = kn (s, C q) for any nonzero constant C , we can just maximize (minimize) over all q such that qT g q = 1. Since kn (s, q) is continuous (recall that the denominator is positive definite), from basic analysis we know that there exists a q1 and q2 that achieves the maximum and minimum, respectively, of kn (s, q). , κ1 = max −qT hq, q∈ 2 , qT g q=1 κ2 = min −qT hq. 53) Because g and h are symmetric and g is positive definite, it can be shown that κ1 and κ2 are the maximum and minimum eigenvalues of the generalized eigenvalue problem: −hq = λg q [12, 68, 70, 81].

Download PDF sample

Algebraic Topology, Homotopy and Homology by R. Switzer


by Joseph
4.3

Rated 4.35 of 5 – based on 42 votes