By William S. Massey

ISBN-10: 038797430X

ISBN-13: 9780387974309

"This ebook is meant to function a textbook for a path in algebraic topology firstly graduate point. the most issues lined are the type of compact 2-manifolds, the elemental team, overlaying areas, singular homology thought, and singular cohomology idea. those themes are built systematically, averting all pointless definitions, terminology, and technical equipment. anywhere attainable, the geometric motivation at the back of many of the ideas is emphasised. The textual content includes fabric from the 1st 5 chapters of the author's past e-book, ALGEBRAIC TOPOLOGY: AN advent (GTM 56), including just about all of the now out-of-print SINGULAR HOMOLOGY concept (GTM 70). the cloth from the sooner books has been rigorously revised, corrected, and taken as much as date."

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**Additional info for A Basic Course in Algebraic Topology (Graduate Texts in Mathematics)**

**Sample text**

Given q = 2e , the q-clan is unique up to equivalence. The Adelaide examples. These are constructed for q = 2e with e even. For the examples with q = 4k , k ≤ 8, that were studied by computer, the group acts transitively on the lines through (∞). S. E. Payne conjectured in [85] that this must be true in general. That conjecture was then proved to be true by W. E. Cherowitzo and S. E. Payne in [22]. Chapter 4 Substructures of Finite Nets Suppose S is a generalized quadrangle of order (s, t), s, t = 1, with a regular point.

The method is taken from S. E. Payne [82]. Let q = 35 . 5. The Other Known Flock GQ’s of Order (q 2, q), q Odd 37 t ∈ GF(q), deﬁne a semiﬁeld ﬂock of the quadratic cone with equation X0 X1 = X22 of PG(3, q). The ﬂock, which is called the Penttila-Williams ﬂock, was constructed by L. Bader, G. Lunardon and I. Pinneri in [4] using the Penttila-Williams ovoid of Q(4, 35 ) deﬁned in [100]. The corresponding GQ, that is, the translation dual of S(F)D , is therefore referred to as the (sporadic) Penttila-Williams generalized quadrangle.

8. If S is isomorphic to a Td (O) with q + 1 points on a line and if S is non-classical, d = 2, 3, then Aut(S) ∼ = PΓL(d + 1, q)O , where O ⊆ PG(2, q) ⊆ PG(3, q) if d = 2, and O ⊆ PG(3, q) ⊆ PG(4, q) if d = 3 (cf. [134]). 3 Generalized Quadrangles of Order (s − 1, s + 1) and (s + 1, s − 1) For each prime power q, R. W. Ahrens and G. Szekeres [1] constructed GQ’s of order (q − 1, q + 1). For q even, these examples were found independently by M. Hall, Jr. [38]. S. E. Payne [68] found a construction method which included all these examples and which produced some additional ones for q even, see [69, 70].

### A Basic Course in Algebraic Topology (Graduate Texts in Mathematics) by William S. Massey

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