# Cohomology Theories

@inproceedings{Brown2010CohomologyT, title={Cohomology Theories}, author={Edgar H. Brown}, year={2010} }

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## 121 Citations

### Notes on the Adams Spectral Sequence

- Mathematics
- 2017

The Adams spectral sequence is a powerful tool for computing homotopy groups of a spectrum, somehow taken with respect to a certain cohomology theory. In particular, it allows one to compute the…

### J ul 2 01 9 The homology of moduli stacks of complexes

- Mathematics
- 2019

We compute the E-homology of the moduli stack M of objects in the derived category of a smooth complex projective variety X, where E is a complex-oriented homology theory with rational coefficient…

### WHAT ARE SPECTRA?

- Mathematics
- 2020

Many algebraic invariants are stable under suspension, for example: the homology, cohomology and stable homotopy groups of a space. To study these, it is useful to work in a “stable” category where…

### Gorenstein duality for Real spectra

- Mathematics
- 2016

Following Hu and Kriz, we study the $C_2$-spectra $BP\mathbb{R}\langle n \rangle$ and $E\mathbb{R}(n)$ that refine the usual truncated Brown-Peterson and the Johnson-Wilson spectra. In particular, we…

### Thus, When It Holds, the Localization Theorem for a Implies a Calculation of Both M (eg + ^ G X) and M (eg + ^ G X) for All Split A-modules M and All Based

- Mathematics

G-spaces X. We must still deene the algebraic construction whose brave new counterpart is given by our completion functors. Returning to the algebraic context of Section 1, we want to deene a…

### Comparison of stratified-algebraic and topological K-theory

- MathematicsJournal of Singularities
- 2020

Stratied-algebra ic vector bundles on real algebraic varieties have many desirable features of algebraic vector bundles but are more exible. We give a characterization of the compact real algebraic…

### GENERALIZED ANDR E-QUILLEN COHOMOLOGY

- Mathematics
- 2008

We explain how the approach of Andr e and Quillen to dening cohomol- ogy and homology as suitable derived functors extends to generalized (co)homology theories, and how this identication may be used…

### Depth and Simplicity of Ohkawa’s Argument

- Mathematics
- 2015

This is an expository article about Ohkawa’s theorem stating that acyclic classes of representable homology theories form a set. We provide background in stable homotopy theory and an overview of…

### An exposition of the topological half of the Grothendieck–Hirzebruch–Riemann–Roch theorem in the fancy language of spectra

- MathematicsExpositiones Mathematicae
- 2021

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Fibre bundles, an integral part of differential geometry, are also important to physics. This text, a succint introduction to fibre bundles, includes such topics as differentiable manifolds and…

### f1 Ky go and ?1 play the role of Zf 1,f2, Sn, C0 and C1. Suppose ?i: go -(S is a covariant functor. Axiom h*. If f and g: X -Y are homotopic, =(f) ==(g)

- f1 Ky go and ?1 play the role of Zf 1,f2, Sn, C0 and C1. Suppose ?i: go -(S is a covariant functor. Axiom h*. If f and g: X -Y are homotopic, =(f) ==(g)

### HOMOLOGY THEORIES AND DUALITY.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
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### First, it is difficult to recover =1(X) from [X, ]; and second, annihilating cohomology classes is more difficult than annihilating homotopy classes

- First, it is difficult to recover =1(X) from [X, ]; and second, annihilating cohomology classes is more difficult than annihilating homotopy classes

### If ir satisfies h*, e* and c*, then there is an Xe 1?, unique up to homotopy type, and a natural equivalence

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### This content downloaded on Thu, 7 Mar 2013 22:50:16 PM All use subject to JSTOR Terms and Conditions

- This content downloaded on Thu, 7 Mar 2013 22:50:16 PM All use subject to JSTOR Terms and Conditions

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### and, by the exact sequence of the triple (SX, X-, x), Hq+l(SX, X-)Hq+l(SX, x0). Clearly all these isomorphisms are natural. Let p be the base point of Sn

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