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Far East Journal of Mathematical Sciences (FJMS)

-manifold. Then the kernel of the forgetful map

considered in this work consists of immersions

nullbordant as a continuous map. Using an exact sequence of normal bordism groups previously given, we present a homological characterization of the kernel of the forgetful map

Also, we prove that

and

are

-isomorphic for

and

-isomorphic for

where

is the class of abelian groups whose elements have order

and

is an orientable stable vector bundle over X.

Far East Journal of Mathematical Sciences (FJMS)
Volume 34, Issue 3, Pages 281 - 288 (September 2009)

REMARKS ON THE NORMAL BORDISM FORGETFUL HOMOMORPHISM
Carlos Biasi (Brazil), Alice K. M. Libardi (Brazil) and Isabel C. Rossini (Brazil)

Abstract:
Assume that X is an oriented smooth

-manifold. Then the kernel of the forgetful map

considered in this work consists of immersions

nullbordant as a continuous map. Using an exact sequence of normal bordism groups previously given, we present a homological characterization of the kernel of the forgetful map

Also, we prove that

and

are

-isomorphic for

and

-isomorphic for

where

is the class of abelian groups whose elements have order

and

is an orientable stable vector bundle over X.

Keywords and phrases: normal bordism, stable homotopy group.

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