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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Preface......................................................................................................5
Introduction...............................................................................................6
1. A class of model categories.................................................................10
1.1 Categories with models......................................................................10
1.2. Cone-complexes...............................................................................12
1.3. Three standard constructions..........................................................14
1.4. Marked cone-complexes and the category Poly...............................16
1.5. Consequences of the marked face structure of a polycell................19
1.6. Subcategories of Poly appropriate as model categories..................23
2. Posets and shellability.........................................................................26
2.1. Shelling............................................................................................26
2.2. The class ET of model categories....................................................29
2.3. Face posets of S-polycells...............................................................32
2.4. The equivalence SPoly → SPos.......................................................36
3. Equivalences of categories of T-complexes.........................................40
3.1. T-complexes.....................................................................................40
3.2. The isomorphism ∆TC → ∆₁TC........................................................42
3.3. Structures and collapsing.................................................................45
3.4. Particular collapses in Sd X and VX..................................................47
3.5. The collapse $A(∆^n)$ in Sd $∆^n - p ∆^n$.......................................55
3.6. The functor $e_ℳ$, from ∆₁T-complexes to ℳ T-complexes...........62
3.7. The natural equivalence $r_ℳ ∘ e_ℳ ≃1$.....................................63
3.8. The equivalence of categories.........................................................65
4. Degeneracy structures in ℳ T-complexes...........................................67
4.1. An approach to degeneracy structures in ℳ T-complexes...............68
4.2. Pseudocylinder structures on SC-complexes...................................70
4.3. Rectifiers on pseudocylinders..........................................................74
4.4. Degenerate elements in an ℳ T-complex........................................77
4.5. Functors between categories of T-complexes..................................83
4.6. Suggested proof of Claims 5.4 and 5.10..........................................86
5. Comments and possibilities for further work........................................92
Appendix. S-shellability of cone-complexes.............................................98
Glossary of symbols..............................................................................106
References...........................................................................................109
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
266
Liczba stron
111
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXVI
Daty
wydano
1988
Twórcy
autor
- Department of Pure Mathematics, University College of North Wales, Bangor, Gwynedd L57 2UW, United Kingdom
Bibliografia
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- [5] N. Ashley, CW posets, preprint, 1982.
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- [8] R. Brown, Non-abelian cohomology and the homotopy classification of maps, preprint, 1982.
- [9] R. Brown, An introduction to simplicial T-complexes, to appear in an issue of Esquisses Math, with the Ph. D. theses of M. K. Dakin.
- [10] R. Brown and P. J. Higgins, The algebra of cubes, J. Pure Appl. Algebra 21 (1981), 233-260.
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- [12] R. Brown and P. J. Higgins, The equivalence of ω-groupoids and cubical T-complexes, Cahiers Topologie Géom. Différentielle 22 (1981), 349 370.
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- [14] R. Brown and P. J. Higgins, Crossed complexes and non-abelian extensions, in Int. Conf. on Category Theory, Gummersbach (1981), Springer. Lecture Notes in Math. 962 (1982), 39-59.
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- [22] M. Evrard, Homotopie des complexes simpliciaux et cubique, preprint.
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- [26] P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory, Ergeb. Math. Grenzgeb. 35, Springer, Berlin 1967.
- [27] V. K. A. M. Gugenheim, On supercomplexes, Trans. Amer. Math. Soc. 85 (1957), 35-51.
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- [31] D. M. Kan, Abstract homotopy I, II, Proc. Nat. Acad. Sci. Washington 41 (1955), 1092-1096 ; 42 (1955), 225-228.
- [32] D. M. Kan, Is an SS complex a CSS complex?, Adv. in Math. 4 (1970), 170-171.
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- [35] A. T. Lundell and S. Weingram, The Topology of CW-complexes, van Nostrand-Reinhold, New York 1969.
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Języki publikacji
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Uwagi
Errata Page, line: 5⁴ For: Asley, 1988 Read: Ashley, 1988
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