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Connected sum

In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classification of closed surfaces.

Connected sum at a point, Connected sum of knots & Connected sum along a codimension-two submanifold

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Connected sum at a point

BallGluing togetherSpheresOrientedUp to
15 related topics

Connected sum of knots

EmbeddingAmbient spaceAmbient isotopyCommutative monoidPrime factorization
12 related topics

Connected sum along a codimension-two submanifold

Euler classesStructure groupCircle groupGroupHomotopy
9 related topics

Connected sum along a submanifold

IsomorphismNormal bundlesNeighborhoodInvolutionNormal vectors
5 related topics

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Overview

Connected sum at a point

Connected sum along a submanifold

Connected sum along a codimension-two submanifold

Local operation

Connected sum of knots

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Map overview Semantic statistics

Connected sum

Nodes55
Edges54
Triples21
Avg. degree1.96
Density0.036364
Components1

How this topic connects Entity context

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Connected sum

Top relations

related to Connected sum of knots · 7
Connected sum → For, However, In, So, There, This, To
related to Connected sum at a point · 6
Connected sum → Although, For, If, Milnor, One, There
related to Connected sum along a submanifold · 3
Connected sum → Let, Suppose, The
related to Local operation · 3
Connected sum → For, The, This
is a · 2
Connected sum → geometric modification on manifolds, local operation on manifolds

Important terminology Word statistics

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Important terminology

sum connected displaystyle knots two manifolds knot along oriented one operation diffeomorphism disjoint also manifold together called orientation construction point

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Connected sumis ageometric modification on manifolds0.90text
Connected sumis alocal operation on manifolds0.90text
Connected sumrelated to Connected sum along a submanifoldThe0.60section
Connected sumrelated to Connected sum along a submanifoldLet0.60section
Connected sumrelated to Connected sum along a submanifoldSuppose0.60section
Connected sumrelated to Connected sum at a pointIf0.60section
Connected sumrelated to Connected sum at a pointAlthough0.60section
Connected sumrelated to Connected sum at a pointOne0.60section
Connected sumrelated to Connected sum at a pointThere0.60section
Connected sumrelated to Connected sum at a pointFor0.60section
Connected sumrelated to Connected sum at a pointMilnor0.60section
Connected sumrelated to Connected sum of knotsThere0.60section

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