By Edwin H. Spanier
Meant to be used either as a textual content and a reference, this publication is an exposition of the elemental principles of algebraic topology. the 1st 3rd of the ebook covers the basic team, its definition and its program within the learn of masking areas. the focal point then turns to homology conception, together with cohomology, cup items, cohomology operations, and topological manifolds. the remainder 3rd of the ebook is dedicated to Homotropy conception, protecting easy proof approximately homotropy teams, functions to obstruction concept, and computations of homotropy teams of spheres. within the later elements, the most emphasis is at the software to geometry of the algebraic instruments constructed previous.
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Additional info for Algebraic Topology '66
This blend of glyceride ethoxylates is prepared by transesteriﬁcation of the whole oils with glycerine followed by ethoxylation (200 and 7 mol on palm and coco, respectively). The end products are then blended in a ratio of about 70:30 to provide balanced multifunctionality in a single product. Figure 8 gives the salt curves for 2% thickener [as PEG-200 hydrogenated glyceryl palmate (and) PEG7 glyceryl cocoate or cocamide DEA], and 12% SLES-2 in water. 44 Dalrymple FIGURE 8 Salt response curve for CDEA and Li S-80.
Chemists began to carefully examine the science behind surfactants and hair care. The original synthetic detergent was found to be extremely irritating, so researchers continued to search for a less irritating detergent. Consumers preferred rich, copious foam, and therefore the development of foam boosters began. The ﬁrst were alkanolamides. Alkanolamides are prepared by reacting a fatty acid with small primary or secondary amines such as monoethanolamine (MEA) or diethanolamine (DEA). The lower fatty acids are most commonly used for shampoo formulations, cocamide MEA being the most common.
Clearly, one would expect that with the actives equal, the C22 derivative of this quaternary would give the highest viscosity response. These results are, however, misleading. The chain length distribution of the quaternaries listed in Table 1 are not equivalent. These data indicate two important inﬂuences controlling viscosity: the chain length and its distribution (purity). As the chain length increases, the viscosity increases given the same purity of the distribution. The balance of the carbon count and the distribution provide the best viscosity behavior in typical cleansing formulations at C16.
Algebraic Topology '66 by Edwin H. Spanier