bundle theorem
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2014 ◽  
Vol 151 (3) ◽  
pp. 461-501 ◽  
Author(s):  
Alexey Ananyevskiy

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.


Author(s):  
Jean Fasel

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


2009 ◽  
Vol 147 (2) ◽  
pp. 295-321
Author(s):  
JYH-HAUR TEH

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.


2001 ◽  
Vol 21 (2) ◽  
pp. 605-635 ◽  
Author(s):  
CLAUDIA WULFF ◽  
JEROEN S. W. LAMB ◽  
IAN MELBOURNE

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.


1996 ◽  
Vol 56 (1-2) ◽  
pp. 87-98 ◽  
Author(s):  
Alexander Kreuzer

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