作者: Spina-Bifida 時間: 2025-3-21 23:20
Graphs,de, in this chapter and elsewhere, into genuine graph-theoretic territory. This may give the reader some idea of the difficult and interesting problems which lie there, but which the main concern of this book, namely homology theory, can scarcely touch.作者: delta-waves 時間: 2025-3-22 03:15 作者: 閃光東本 時間: 2025-3-22 08:34 作者: Introvert 時間: 2025-3-22 09:11 作者: CRAFT 時間: 2025-3-22 14:04 作者: CRAFT 時間: 2025-3-22 20:47
Some general theorems,ate the homology groups of some other standard simplicial complexes such as cones (6.8) and spheres (6.11(3)), and show (6.10) that relative homology groups can be defined in terms of ordinary homology groups.作者: Landlocked 時間: 2025-3-22 21:23 作者: PLUMP 時間: 2025-3-23 02:16 作者: 種族被根除 時間: 2025-3-23 09:09 作者: carotenoids 時間: 2025-3-23 12:15 作者: constitutional 時間: 2025-3-23 15:22 作者: GULF 時間: 2025-3-23 21:11
The question of invariance,ng the “compactness” of |K|. See Kelley (1955), p.141.) The stronger assertion is referred to as the topological invariance of homology groups: it says that homology groups do not depend on particular triangulations but only on the unierlying topological structure of |K|.作者: Nutrient 時間: 2025-3-24 00:02
Two more general theorems,rs can be stuck together to give either a torus or a Klein bottle (see 7.5). The result is not an explicit formula for H (L ? L.) but an exact sequence which, with luck, will give a good deal of information. An example where it does not give quite enough information to determine a homology group of L. ?L. is mentioned in 7.6(3).作者: 花費 時間: 2025-3-24 02:39
https://doi.org/10.1007/978-2-8178-0239-8 shall, as described in the Introduction, assume that they are divided up into triangles.? It is therefore necessary at the outset to pinpoint the decisive property which an object must possess in order to be called a surface, and to interpret this as a property of the triangulation.作者: Scleroderma 時間: 2025-3-24 07:22 作者: forestry 時間: 2025-3-24 10:51
https://doi.org/10.1007/978-3-662-08816-6e. To be a little more precise, let M be a closed surface and let K be a graph which is a sub- complex of M. If K is removed from M, what is left is a number of disjoint subsets of M which we refer to as the “regions” into which K divides M. (Alternatively we may picture M as being cut along K: it falls into separate pieces, one for each region.)作者: GULLY 時間: 2025-3-24 15:21
Closed surfaces, shall, as described in the Introduction, assume that they are divided up into triangles.? It is therefore necessary at the outset to pinpoint the decisive property which an object must possess in order to be called a surface, and to interpret this as a property of the triangulation.作者: 新義 時間: 2025-3-24 19:02 作者: Lyme-disease 時間: 2025-3-25 02:42
Graphs in surfaces,e. To be a little more precise, let M be a closed surface and let K be a graph which is a sub- complex of M. If K is removed from M, what is left is a number of disjoint subsets of M which we refer to as the “regions” into which K divides M. (Alternatively we may picture M as being cut along K: it falls into separate pieces, one for each region.)作者: 等待 時間: 2025-3-25 06:27 作者: 土坯 時間: 2025-3-25 09:55
Graphs,reader is referred to books of Harary (1967), Harris ( 1970) and Busacker and Saaty (1965) for evidence to support this claim, since our motivation for touching on the subject here is different. Many of the ideas which we shall encounter later can be met, in a diluted form, in the simpler situation 作者: 檢查 時間: 2025-3-25 14:31 作者: Estimable 時間: 2025-3-25 17:21 作者: 高興去去 時間: 2025-3-26 00:02 作者: 圓木可阻礙 時間: 2025-3-26 03:40 作者: Instantaneous 時間: 2025-3-26 05:22 作者: HUSH 時間: 2025-3-26 08:39 作者: diskitis 時間: 2025-3-26 14:26
Homology modulo 2,y so that it applies to unoriented simplicial complexes. Roughly speaking if an oriented simplex a and the same simplex with opposite orientation, -σ, are to be regarded as giving the same chain, then ?1 = +1 and so the coefficients must be regarded as lying in the group (or field) ZZ. instead of in作者: chuckle 時間: 2025-3-26 18:06 作者: 小故事 時間: 2025-3-27 00:30 作者: Minatory 時間: 2025-3-27 04:16
https://doi.org/10.1007/978-2-287-09416-3reader is referred to books of Harary (1967), Harris ( 1970) and Busacker and Saaty (1965) for evidence to support this claim, since our motivation for touching on the subject here is different. Many of the ideas which we shall encounter later can be met, in a diluted form, in the simpler situation 作者: 愚蠢人 時間: 2025-3-27 09:22 作者: 執(zhí) 時間: 2025-3-27 12:19
https://doi.org/10.1007/978-4-431-68111-3eader has come across triangles before. Nevertheless a precise definition in terms suited to our purpose is given below, where triangles appear under the alias of “2-simplexes”. The precise definition makes it clear that “triangle” is a good way to coiainue the sequence “point, segment, …” (which be作者: 形容詞 時間: 2025-3-27 16:50
https://doi.org/10.1007/978-3-662-63610-7There is one group, H.(K), in each dimension p with 0 ? p ? dim K; the group H (K) measures, roughly speaking, the number of “independent p-dimensional holes” in K. If K is an oriented graph then H.(K) is isomorphic to the group Z.(K) of 1-cycles on K (see 1.19).作者: 忘川河 時間: 2025-3-27 20:40
https://doi.org/10.1007/978-2-287-33744-4hat K and K. are simplicial complexes triangulating the same object, i.e. with |K|= |K.|. Is it true that H. (K) ? H. (K.) for all p ? The answer is in fact “yes” — indeed a stronger assertion (5.13) is true, namely that the isomorphisms hold if |K|v is merely supposed homeomorphic to |K.|, i.e. if 作者: 東西 時間: 2025-3-27 22:27
https://doi.org/10.1007/978-88-470-0496-2evident difficulty of calculating homology groups directly from the definition, and the consequent need for some help from general theorems. Enough is proved here to enable us to calculate the homology groups of all the closed surfaces described in Chapter 2, without difficulty. We shall also calcul作者: cajole 時間: 2025-3-28 04:49 作者: Laconic 時間: 2025-3-28 06:49
John Fauvel,Raymond Flood,Robin Wilsony so that it applies to unoriented simplicial complexes. Roughly speaking if an oriented simplex a and the same simplex with opposite orientation, -σ, are to be regarded as giving the same chain, then ?1 = +1 and so the coefficients must be regarded as lying in the group (or field) ZZ. instead of in作者: 尖牙 時間: 2025-3-28 13:36
https://doi.org/10.1007/978-3-662-08816-6e. To be a little more precise, let M be a closed surface and let K be a graph which is a sub- complex of M. If K is removed from M, what is left is a number of disjoint subsets of M which we refer to as the “regions” into which K divides M. (Alternatively we may picture M as being cut along K: it f作者: fetter 時間: 2025-3-28 15:30 作者: 孤僻 時間: 2025-3-28 22:28 作者: 樹上結(jié)蜜糖 時間: 2025-3-29 00:51 作者: 輕觸 時間: 2025-3-29 07:01
Michael St.Pierrefiken und Farbfotos.Alle für Therapeuten relevanten medizini.Physiotherapeuten, Masseure und Ergotherapeuten finden in diesem 2b?ndigen Lehrbuch alles, was sie über die moderne "Komplexe physikalische Entstauungstherapie" und ihre praktische Anwendung wissen sollten. Mit dem hier vermittelten Praxis作者: Substance-Abuse 時間: 2025-3-29 09:57
