Stable classification of manifolds
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1 Introduction
Tex syntax errorsuch that is diffeomorphic to . By we mean the connected sum with
Tex syntax errorcopies of . Note that since has an orientation reversing diffeomorphism the connect sum with it is well defined (see Parametric connected sum). We present a method which reduces the stable classification to a bordism problem.
2 The normal k-type
Tex syntax error-factorization
Tex syntax error-connected, i.e. the homotopy groups of the fibre vanish in degree , and the map is an
Tex syntax error-equivalence.
Definition 1.1. The fibre homotopy type of the fibration is an invariant of the map and is called the normal -type of denoted [Kreck1999].
For example the normal -type of an oriented manifold is the universal covering
If
References
- [Kreck1999] M. Kreck, Surgery and duality, Ann. of Math. (2) 149 (1999), no.3, 707–754. MR1709301 (2001a:57051) Zbl 0935.57039
- [Spanier1981] E. H. Spanier, Algebraic topology, Springer-Verlag, 1981. MR666554 (83i:55001) Zbl 0810.55001
Tex syntax errorsuch that is diffeomorphic to . By we mean the connected sum with
Tex syntax errorcopies of . Note that since has an orientation reversing diffeomorphism the connect sum with it is well defined (see Parametric connected sum). We present a method which reduces the stable classification to a bordism problem.
2 The normal k-type
Tex syntax error-factorization
Tex syntax error-connected, i.e. the homotopy groups of the fibre vanish in degree , and the map is an
Tex syntax error-equivalence.
Definition 1.1. The fibre homotopy type of the fibration is an invariant of the map and is called the normal -type of denoted [Kreck1999].
For example the normal -type of an oriented manifold is the universal covering
If
References
- [Kreck1999] M. Kreck, Surgery and duality, Ann. of Math. (2) 149 (1999), no.3, 707–754. MR1709301 (2001a:57051) Zbl 0935.57039
- [Spanier1981] E. H. Spanier, Algebraic topology, Springer-Verlag, 1981. MR666554 (83i:55001) Zbl 0810.55001
Tex syntax errorsuch that is diffeomorphic to . By we mean the connected sum with
Tex syntax errorcopies of . Note that since has an orientation reversing diffeomorphism the connect sum with it is well defined (see Parametric connected sum). We present a method which reduces the stable classification to a bordism problem.
2 The normal k-type
Tex syntax error-factorization
Tex syntax error-connected, i.e. the homotopy groups of the fibre vanish in degree , and the map is an
Tex syntax error-equivalence.
Definition 1.1. The fibre homotopy type of the fibration is an invariant of the map and is called the normal -type of denoted [Kreck1999].
For example the normal -type of an oriented manifold is the universal covering
If
References
- [Kreck1999] M. Kreck, Surgery and duality, Ann. of Math. (2) 149 (1999), no.3, 707–754. MR1709301 (2001a:57051) Zbl 0935.57039
- [Spanier1981] E. H. Spanier, Algebraic topology, Springer-Verlag, 1981. MR666554 (83i:55001) Zbl 0810.55001
Tex syntax errorsuch that is diffeomorphic to . By we mean the connected sum with
Tex syntax errorcopies of . Note that since has an orientation reversing diffeomorphism the connect sum with it is well defined (see Parametric connected sum). We present a method which reduces the stable classification to a bordism problem.
2 The normal k-type
Tex syntax error-factorization
Tex syntax error-connected, i.e. the homotopy groups of the fibre vanish in degree , and the map is an
Tex syntax error-equivalence.
Definition 1.1. The fibre homotopy type of the fibration is an invariant of the map and is called the normal -type of denoted [Kreck1999].
For example the normal -type of an oriented manifold is the universal covering
If
References
- [Kreck1999] M. Kreck, Surgery and duality, Ann. of Math. (2) 149 (1999), no.3, 707–754. MR1709301 (2001a:57051) Zbl 0935.57039
- [Spanier1981] E. H. Spanier, Algebraic topology, Springer-Verlag, 1981. MR666554 (83i:55001) Zbl 0810.55001
Tex syntax errorsuch that is diffeomorphic to . By we mean the connected sum with
Tex syntax errorcopies of . Note that since has an orientation reversing diffeomorphism the connect sum with it is well defined (see Parametric connected sum). We present a method which reduces the stable classification to a bordism problem.
2 The normal k-type
Tex syntax error-factorization
Tex syntax error-connected, i.e. the homotopy groups of the fibre vanish in degree , and the map is an
Tex syntax error-equivalence.
Definition 1.1. The fibre homotopy type of the fibration is an invariant of the map and is called the normal -type of denoted [Kreck1999].
For example the normal -type of an oriented manifold is the universal covering
If
References
- [Kreck1999] M. Kreck, Surgery and duality, Ann. of Math. (2) 149 (1999), no.3, 707–754. MR1709301 (2001a:57051) Zbl 0935.57039
- [Spanier1981] E. H. Spanier, Algebraic topology, Springer-Verlag, 1981. MR666554 (83i:55001) Zbl 0810.55001
Tex syntax errorsuch that is diffeomorphic to . By we mean the connected sum with
Tex syntax errorcopies of . Note that since has an orientation reversing diffeomorphism the connect sum with it is well defined (see Parametric connected sum). We present a method which reduces the stable classification to a bordism problem.
2 The normal k-type
Tex syntax error-factorization
Tex syntax error-connected, i.e. the homotopy groups of the fibre vanish in degree , and the map is an
Tex syntax error-equivalence.
Definition 1.1. The fibre homotopy type of the fibration is an invariant of the map and is called the normal -type of denoted [Kreck1999].
For example the normal -type of an oriented manifold is the universal covering
If
References
- [Kreck1999] M. Kreck, Surgery and duality, Ann. of Math. (2) 149 (1999), no.3, 707–754. MR1709301 (2001a:57051) Zbl 0935.57039
- [Spanier1981] E. H. Spanier, Algebraic topology, Springer-Verlag, 1981. MR666554 (83i:55001) Zbl 0810.55001