Inertial hcobordisms

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Title 
Inertial hcobordisms 
Author 
Renegar, Cynthia Diane 
School 
Tulane University 
Academic Field 
Mathematics 
Abstract 
It is known that an hcobordism from M #(,r)(S('p) x S('q)), dim M (GREATERTHEQ) 5, 2 (LESSTHEQ) p (LESSTHEQ) dim M2 is inertial provided the torsion of the hcobordism can be represented by an r x r matrix. In this paper we generalize this result and show that, in fact, the hcobordism can be surgered to a product cobordism. The techniques do not involve the surgery obstruction groups of C.T.C. Wall as the above class contains hcobordisms for which the surgery obstruction element associated to the hcobordism by means of the Rothenberg sequence is nonzero We introduce an algebraic condition on the torsion of the hcobordism which guarantees the hcobordism is inertial provided the dimension of the hcobordism is 7 or 15. Here again the hcobordism can be surgered to a product cobordism, and the techniques do not involve the surgery obstruction groups of C.T.C. Wall. These groups take into account only those properties possessed by all manifolds which differ by 4n dimensions whereas the techniques here rely on the fact that the dimension of the hcobordism is 7 or 15 Finally, if the torsion of the hcobordism (W;M,N) satisfies (tau) = (1)('dim) ('W)(tau)*, for M(,0) a codimension one submanifold of M having the same fundamental group, N is obtained from M by splitting along M(,0) and regluing by an isomorphism h which is described geometrically for a class of hcobordisms characterized by an algebraic condition on the torsion, provided the dimension of the hcobordism is 2n + 1, n (GREATERTHEQ) 3 
Language 
eng 
Degree Date 
1985 
Degree 
Ph.D 
Publisher 
Tulane University 
Publication Date 
1985 
Source 
64 p., Dissertation Abstracts International, Volume: 4701, Section: B, page: 0243 
Identifier 
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Rights 
Copyright is in accordance with U.S. Copyright law 
Contact Information 
acase@tulane.edu 
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