Chern rank of complex bundle

Bikram Banerjee

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 3, page 401-413
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Banerjee, Bikram. "Chern rank of complex bundle." Commentationes Mathematicae Universitatis Carolinae 60.3 (2019): 401-413. <http://eudml.org/doc/294732>.

@article{Banerjee2019,
abstract = {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.},
author = {Banerjee, Bikram},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Chern class; characteristic rank; cup length; chern rank},
language = {eng},
number = {3},
pages = {401-413},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Chern rank of complex bundle},
url = {http://eudml.org/doc/294732},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Banerjee, Bikram
TI - Chern rank of complex bundle
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 3
SP - 401
EP - 413
AB - 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.
LA - eng
KW - Chern class; characteristic rank; cup length; chern rank
UR - http://eudml.org/doc/294732
ER -

References

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  6. Naolekar A. C., 10.2478/s12175-012-0057-2, Math. Slovaca 62 (2012), no. 5, 949–966. MR2981832DOI10.2478/s12175-012-0057-2
  7. Naolekar A. C., Thakur A. S., 10.2478/s12175-014-0289-4, Math. Slovaca 64 (2014), no. 6, 1525–1540. MR3298036DOI10.2478/s12175-014-0289-4

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