Finite inversive planes satisfying the bundle theorem

1982 ◽  
Vol 12 (2) ◽  
Author(s):  
Jeff Kahn
Keyword(s):  
Bundle Theorem

The projective bundle theorem for Ij -cohomology

2013 ◽  
Vol 11 (2) ◽  
pp. 413-464 ◽  
Author(s):  
Jean Fasel
Keyword(s):  
Projective Bundle ◽  
Bundle Theorem

AbstractWe compute the total Ij -cohomology of a projective bundle over a smooth scheme.

scholarly journals The special linear version of the projective bundle theorem

2014 ◽  
Vol 151 (3) ◽  
pp. 461-501 ◽  
Author(s):  
Alexey Ananyevskiy
Keyword(s):  
Polynomial Algebra ◽  
Characteristic Classes ◽  
Zero Section ◽  
Grassmann Variety ◽  
Special Linear ◽  
Bundle Theorem ◽  
Linear Version ◽  
Hopf Map ◽  
Ring Cohomology ◽  
Witt Groups

AbstractA special linear Grassmann variety $\text{SGr}(k,n)$ is the complement to the zero section of the determinant of the tautological vector bundle over $\text{Gr}(k,n)$. For an $SL$-oriented representable ring cohomology theory $A^{\ast }(-)$ with invertible stable Hopf map ${\it\eta}$, including Witt groups and $\text{MSL}_{{\it\eta}}^{\ast ,\ast }$, we have $A^{\ast }(\text{SGr}(2,2n+1))\cong A^{\ast }(pt)[e]/(e^{2n})$, and $A^{\ast }(\text{SGr}(k,n))$ is a truncated polynomial algebra over $A^{\ast }(pt)$ whenever $k(n-k)$ is even. A splitting principle for such theories is established. Using the computations for the special linear Grassmann varieties, we obtain a description of $A^{\ast }(\text{BSL}_{n})$ in terms of homogeneous power series in certain characteristic classes of tautological bundles.

A fiber bundle theorem

1992 ◽  
Vol 76 (1) ◽  
pp. 105-110 ◽  
Author(s):  
Helmut Reckziegel
Keyword(s):  
Fiber Bundle ◽  
Bundle Theorem

Locally projective spaces which satisfy the Bundle Theorem

1996 ◽  
Vol 56 (1-2) ◽  
pp. 87-98 ◽  
Author(s):  
Alexander Kreuzer
Keyword(s):  
Projective Spaces ◽  
Bundle Theorem

scholarly journals Bifurcation from relative periodic solutions

2001 ◽  
Vol 21 (2) ◽  
pp. 605-635 ◽  
Author(s):  
CLAUDIA WULFF ◽  
JEROEN S. W. LAMB ◽  
IAN MELBOURNE
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Systematic Approach ◽  
Local Bifurcation ◽  
Dimensional Problem ◽  
Continuous Symmetry ◽  
Finite Dimensional ◽  
Bundle Theorem ◽  
Spatiotemporal Symmetries

Relative periodic solutions are ubiquitous in dynamical systems with continuous symmetry. Recently, Sandstede, Scheel and Wulff derived a center bundle theorem, reducing local bifurcation from relative periodic solutions to a finite-dimensional problem. Independently, Lamb and Melbourne showed how to systematically study local bifurcation from isolated periodic solutions with discrete spatiotemporal symmetries.In this paper, we show how the center bundle theorem, when combined with certain group theoretic results, reduces bifurcation from relative periodic solutions to bifurcation from isolated periodic solutions. In this way, we obtain a systematic approach to the study of local bifurcation from relative periodic solutions.

scholarly journals Motivic integration and projective bundle theorem in morphic cohomology

2009 ◽  
Vol 147 (2) ◽  
pp. 295-321
Author(s):  
JYH-HAUR TEH
Keyword(s):  
Algebraic Cycles ◽  
Motivic Integration ◽  
Projective Bundle ◽  
Cohomology Groups ◽  
Hodge Conjecture ◽  
Projective Varieties ◽  
Bundle Theorem

AbstractWe reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two K-equivalent varieties are the same, which implies that several conjectures of algebraic cycles are K-statements. We define stringy functions which enable us to ask stringy Grothendieck standard conjecture and stringy Hodge conjecture. We prove a projective bundle theorem in morphic cohomology for trivial bundles over any normal quasi-projective varieties.

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