scholarly journals On vector bundles for a Morse decomposition of $L\mathbb{C}\mathrm{P}^n$

2017 ◽  
Vol 121 (2) ◽  
pp. 186
Author(s):  
Iver Ottosen
Keyword(s):  
Loop Space ◽  
Vector Bundles ◽  
Morse Decomposition ◽  
Energy Integral ◽  
Chern Classes ◽  
Free Loop Space ◽  
Stiefel Manifolds ◽  
Mod P

We give a description of the negative bundles for the energy integral on the free loop space $L\mathbb{C}\mathrm{P}^n$ in terms of circle vector bundles over projective Stiefel manifolds. We compute the mod $p$ Chern classes of the associated homotopy orbit bundles.

scholarly journals A Construction of Chern Classes of Parabolic Vector Bundles

2013 ◽  
Vol 42 (3) ◽  
pp. 1111-1122 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon
Keyword(s):  
Vector Bundles ◽  
Chern Classes

scholarly journals Morava $K$-theory and the free loop space

1992 ◽  
Vol 114 (1) ◽  
pp. 243-243
Author(s):  
John McCleary ◽  
Dennis A. McLaughlin
Keyword(s):  
Loop Space ◽  
Free Loop Space ◽  
K Theory

scholarly journals Chern classes of tensor products

2016 ◽  
Vol 27 (10) ◽  
pp. 1650079 ◽  
Author(s):  
Laurent Manivel
Keyword(s):  
Vector Bundles ◽  
Tensor Products ◽  
Chern Classes ◽  
Explicit Formulas

We prove explicit formulas for Chern classes of tensor products of virtual vector bundles, whose coefficients are given by certain universal polynomials in the ranks of the two bundles.

scholarly journals A Spectral Sequence for the Hochschild Cohomology of a Coconnective DGA

2013 ◽  
Vol 112 (2) ◽  
pp. 182 ◽  
Author(s):  
Shoham Shamir
Keyword(s):  
Spectral Sequence ◽  
Loop Space ◽  
Hochschild Cohomology ◽  
Derived Category ◽  
Orientable Manifold ◽  
Support Varieties ◽  
Mod P

A spectral sequence for the computation of the Hochschild cohomology of a coconnective dga over a field is presented. This spectral sequence has a similar flavour to the spectral sequence presented in [7] for the computation of the loop homology of a closed orientable manifold. Using this spectral sequence we identify a class of spaces for which the Hochschild cohomology of their mod-$p$ cochain algebra is Noetherian. This implies, among other things, that for such a space the derived category of mod-$p$ chains on its loop-space carries a theory of support varieties.

Vector Bundles and Chern Classes

1984 ◽  
pp. 47-69
Author(s):  
William Fulton
Keyword(s):  
Vector Bundles ◽  
Chern Classes

scholarly journals OBSTRUCTIONS TO ALGEBRAIZING TOPOLOGICAL VECTOR BUNDLES

2019 ◽  
Vol 7 ◽  
Author(s):  
A. ASOK ◽  
J. FASEL ◽  
M. J. HOPKINS
Keyword(s):  
Vector Bundle ◽  
Complex Manifold ◽  
Algebraic Variety ◽  
Vector Bundles ◽  
Necessary Condition ◽  
Chern Classes ◽  
Smooth Complex ◽  
Steenrod Operations ◽  
Complex Algebraic Variety ◽  
Cycle Class

Suppose $X$ is a smooth complex algebraic variety. A necessary condition for a complex topological vector bundle on $X$ (viewed as a complex manifold) to be algebraic is that all Chern classes must be algebraic cohomology classes, that is, lie in the image of the cycle class map. We analyze the question of whether algebraicity of Chern classes is sufficient to guarantee algebraizability of complex topological vector bundles. For affine varieties of dimension ${\leqslant}3$, it is known that algebraicity of Chern classes of a vector bundle guarantees algebraizability of the vector bundle. In contrast, we show in dimension ${\geqslant}4$ that algebraicity of Chern classes is insufficient to guarantee algebraizability of vector bundles. To do this, we construct a new obstruction to algebraizability using Steenrod operations on Chow groups. By means of an explicit example, we observe that our obstruction is nontrivial in general.

The Exponential Map on the Free Loop Space is Fredholm

1997 ◽  
Vol 7 (5) ◽  
pp. 954-969 ◽  
Author(s):  
G. Misio?ek
Keyword(s):  
Loop Space ◽  
Exponential Map ◽  
Free Loop Space

Ample vector bundles, Chern classes, and numerical criteria

1976 ◽  
Vol 32 (2) ◽  
pp. 171-178 ◽  
Author(s):  
William Fulton
Keyword(s):  
Vector Bundles ◽  
Chern Classes

scholarly journals On the geometry of free loop spaces

2002 ◽  
Vol 30 (1) ◽  
pp. 15-23 ◽  
Author(s):  
P. Manoharan
Keyword(s):  
Fundamental Form ◽  
Open Subset ◽  
Loop Space ◽  
Free Loop Space ◽  
Loop Spaces ◽  
Central Extensions ◽  
Christoffel Symbols

We verify the following three basic results on the free loop spaceLM. (1) We show that the set of all points, where the fundamental form onLMis nondegenerate, is an open subset. (2) The connections of a Fréchet bundle overLMcan be extended toS1-central extensions and, in particular, there exist natural connections on the string structures. (3) The notion of Christoffel symbols and the curvature are introduced onLMand they are described in terms of Christoffel symbols ofM.

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