What is a non-bounding cycle in homology?

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I came across this term "non-bounding" cycle in the context of homology. However I am not exactly sure what it means.



What I know is that cycles are element of $kerpartial_k$ and boundaries are elements of $im partial_k+1$. So my guess is that non-bounding cycle is a cycle that is not a boundary?



Thanks for any help.




algebraic-topology homology-cohomology




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    up vote
    1
    down vote

    favorite












    I came across this term "non-bounding" cycle in the context of homology. However I am not exactly sure what it means.



    What I know is that cycles are element of $kerpartial_k$ and boundaries are elements of $im partial_k+1$. So my guess is that non-bounding cycle is a cycle that is not a boundary?



    Thanks for any help.




    algebraic-topology homology-cohomology




    share|cite|improve this question






















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I came across this term "non-bounding" cycle in the context of homology. However I am not exactly sure what it means.



      What I know is that cycles are element of $kerpartial_k$ and boundaries are elements of $im partial_k+1$. So my guess is that non-bounding cycle is a cycle that is not a boundary?



      Thanks for any help.




      algebraic-topology homology-cohomology




      share|cite|improve this question












      I came across this term "non-bounding" cycle in the context of homology. However I am not exactly sure what it means.



      What I know is that cycles are element of $kerpartial_k$ and boundaries are elements of $im partial_k+1$. So my guess is that non-bounding cycle is a cycle that is not a boundary?



      Thanks for any help.





      algebraic-topology homology-cohomology





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      share|cite|improve this question




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      asked Feb 24 '17 at 8:21









      yoyostein

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          Examples of non-bounding cycles are toroidal or poloidal closed loops on a torus that do not enclose any area. Compare with closed loops on a spere all of which are bounding cycles.






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            up vote
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            accepted










            Examples of non-bounding cycles are toroidal or poloidal closed loops on a torus that do not enclose any area. Compare with closed loops on a spere all of which are bounding cycles.






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              up vote
              1
              down vote



              accepted










              Examples of non-bounding cycles are toroidal or poloidal closed loops on a torus that do not enclose any area. Compare with closed loops on a spere all of which are bounding cycles.






              share|cite|improve this answer






















                up vote
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                accepted







                up vote
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                down vote



                accepted






                Examples of non-bounding cycles are toroidal or poloidal closed loops on a torus that do not enclose any area. Compare with closed loops on a spere all of which are bounding cycles.






                share|cite|improve this answer












                Examples of non-bounding cycles are toroidal or poloidal closed loops on a torus that do not enclose any area. Compare with closed loops on a spere all of which are bounding cycles.







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                answered Mar 21 '17 at 11:54









                Subir Ghosh

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