| Title:
|
Chern rank of complex bundle (English) |
| Author:
|
Banerjee, Bikram |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
401-413 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Motivated by the work of A.\,C. Naolekar and A.\,S. Thakur (2014) we introduce notions of upper chern rank and even cup length of a finite connected CW-complex and prove that upper chern rank is a homotopy invariant. It turns out that determination of upper chern rank of a space $X$ sometimes helps to detect whether a generator of the top cohomology group can be realized as Euler class for some real (orientable) vector bundle over $X$ or not. For a closed connected $d$-dimensional complex manifold we obtain an upper bound of its even cup length. For a finite connected even dimensional CW-complex with its upper chern rank equal to its dimension, we provide a method of computing its even cup length. Finally, we compute upper chern rank of many interesting spaces. (English) |
| Keyword:
|
Chern class |
| Keyword:
|
characteristic rank |
| Keyword:
|
cup length |
| Keyword:
|
chern rank |
| MSC:
|
57R20 |
| idZBL:
|
Zbl 07144902 |
| idMR:
|
MR4034440 |
| DOI:
|
10.14712/1213-7243.2019.015 |
| . |
| Date available:
|
2019-10-29T13:02:39Z |
| Last updated:
|
2021-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147858 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
