Պահպանված է:
| Հիմնական հեղինակներ: | , |
|---|---|
| Ձևաչափ: | Preprint |
| Հրապարակվել է: |
2011
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| Խորագրեր: | |
| Առցանց հասանելիություն: | https://arxiv.org/abs/1106.0412 |
| Ցուցիչներ: |
Ավելացրեք ցուցիչ
Չկան պիտակներ, Եղեք առաջինը, ով նշում է այս գրառումը!
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Բովանդակություն:
- James' sectional category and Farber's topological complexity are studied in a general and unified framework. We introduce `relative' and `strong relative' forms of the category for a map. We show that both can differ from sectional category just by 1. A map has sectional or relative category less than or equal to $n$ if, and only if, it is `dominated' (in some sense) by a map with strong relative category less than or equal to $n$. A homotopy pushout can increase sectional category but neither homotopy pushouts, nor homotopy pullbacks, can increase (strong) relative category. This makes (strong) relative category a convenient tool to study sectional category. We completely determine the sectional and relative categories of the fibres of the Ganea fibrations. As a particular case, the `topological complexity' of a space is the sectional category of the diagonal map. So it can differ from the (strong) relative category of the diagonal just by 1. We call the strong relative category of the diagonal `strong complexity'. We show that the strong complexity of a suspension is at most 2.