Cohomology Theories

@inproceedings{Brown2010CohomologyT,
  title={Cohomology Theories},
  author={Edgar H. Brown},
  year={2010}
}
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121 Citations
Highly Influential Citations
5
Background Citations
29
Methods Citations
12

121 Citations

Notes on the Adams Spectral Sequence

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

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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

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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…

A freeness theorem for RO(Z/2)-graded cohomology

Comparison of stratified-algebraic and topological K-theory

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

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

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

...

References

SHOWING 1-10 OF 11 REFERENCES

Topology of Fibre Bundles

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)

Review: Norman Steenrod, The topology of fibre bundles

Foundations of Algebraic Topology

HOMOLOGY THEORIES AND DUALITY.

  • G. Whitehead
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1960

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

  • BRANDEIS UNIVERSITY BIBLIOGRAPHY

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

On spaces having the same homotopy type as a Cw-complex

  • Trans. Amer. Math. Soc
  • 1959

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

  • By excision, Hq(p) Hq(SO