کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9505928 | 1340362 | 2005 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Dipaths and dihomotopies in a cubical complex
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
In the geometric realization of a cubical complex without degeneracies, a â¡-set, dipaths and dihomotopies may not be combinatorial, i.e., not geometric realizations of combinatorial dipaths and equivalences. When we want to use geometric/topological tools to classify dipaths on the 1-skeleton, combinatorial dipaths, up to dihomotopy, and in particular up to combinatorial dihomotopy, we need that all dipaths are in fact dihomotopic to a combinatorial dipath. And moreover that two combinatorial dipaths which are dihomotopic are then combinatorially dihomotopic. We prove that any dipath from a vertex to a vertex is dihomotopic to a combinatorial dipath, in a non-selfintersecting â¡-set. And that two combinatorial dipaths which are dihomotopic through a non-combinatorial dihomotopy are in fact combinatorially dihomotopic, in a geometric â¡-set. Moreover, we prove that in a geometric â¡-set, the d-homotopy introduced in [M. Grandis, Directed homotopy theory, I, Cah. Topol. Géom. Différ. Catég. 44 (4) (2003) 281-316] coincides with the dihomotopy in [L. Fajstrup, E. Goubault, M. Raussen, Algebraic topology and concurrency, Theoret. Comput. Sci., in press; also technical report, Aalborg University, 1999].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Applied Mathematics - Volume 35, Issue 2, August 2005, Pages 188-206
Journal: Advances in Applied Mathematics - Volume 35, Issue 2, August 2005, Pages 188-206
نویسندگان
Lisbeth Fajstrup,