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55Sxx Operations and obstructions

This subtopic introduces the core ideas in operations and obstructions, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

55S05 Primary cohomology operations in algebraic topology

Overview

Primary cohomology operations in algebraic topology. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S10 Steenrod algebra

Overview

Steenrod algebra. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S12 Dyer-Lashof operations

Overview

Dyer-Lashof operations. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S15 Symmetric products and power spaces

Overview

Symmetric products and power spaces. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S20 Secondary and higher cohomology operations in algebraic topology

Overview

Secondary and higher cohomology operations in algebraic topology. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S25 $K$-theory operations and generalized cohomology operations in algebraic topology

Overview

$K$-theory operations and generalized cohomology operations in algebraic topology. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S30 Massey products

Overview

Massey products. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S35 Obstruction theory in algebraic topology

Overview

Obstruction theory in algebraic topology. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S36 Extension and lifting problems in algebraic topology

Overview

Extension and lifting problems in algebraic topology. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S37 Classification of mappings in algebraic topology

Overview

Classification of mappings in algebraic topology. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S40 Sectioning fiber spaces and bundles

Overview

Sectioning fiber spaces and bundles. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S45 Postnikov systems, $k$-invariants

Overview

Postnikov systems, $k$-invariants. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks

55S91 Equivariant operations and obstructions in algebraic topology

Overview

Equivariant operations and obstructions in algebraic topology. This topic covers operations and obstructions in algebraic topology, including cohomology operations and extension/lifting criteria.

Related Wikipedia Page

Wikipedia: Cohomology operation

Useful Links

Key Ideas

  • Steenrod and related operations
  • obstruction classes and lifting
  • secondary and higher operations

Typical Uses

Used to determine existence and uniqueness of topological constructions under compatibility constraints.

Applications

  • Bundle and map classification
  • Homotopy computations
  • Topological realization problems

References

Recommended Textbooks