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Full-Text Articles in Physical Sciences and Mathematics
On Simplicial Commutative Algebras With Noetherian Homotopy, James M. Turner
On Simplicial Commutative Algebras With Noetherian Homotopy, James M. Turner
University Faculty Publications and Creative Works
In this paper, we introduce a strategy for studying simplicial commutative algebras over general commutative rings R. Given such a simplicial algebra A, this strategy involves replacing A with a connected simplicial commutative k(℘)-algebra A(℘), for each ℘ ε Spec(π0A), which we call the connected component of A at ℘. These components retain most of the André-Quillen homology of A when the coefficients are k(℘)-modules (k(℘)=residue field of ℘ in π0A). Thus, these components should carry quite a bit of the homotopy theoretic information for A. Our aim will be to apply this strategy to those simplicial algebras which possess …
The Mathematics Of T. Benny Rushing, James Keesling, Luis Montejano, Gerard A. Venema
The Mathematics Of T. Benny Rushing, James Keesling, Luis Montejano, Gerard A. Venema
University Faculty Publications and Creative Works
No abstract provided.
Representing Homology Classes Of Simply Connected 4-Manifolds, Vo Thanh Liem, Gerard A. Venema
Representing Homology Classes Of Simply Connected 4-Manifolds, Vo Thanh Liem, Gerard A. Venema
University Faculty Publications and Creative Works
The main theorem asserts that every 2-dimensional homology class of a compact simply connected PL 4-manifold can be represented by a codimension-0 submanifold consisting of a contractible manifold with a single 2-handle attached. One consequence of the theorem is the fact that every map of S2 into a simply connected, compact PL 4-manifold is homotopic to an embedding if and only if the same is true for every homotopy equivalence. The theorem is also the main ingredient in the proof of the following result: If W is a compact, simply connected, PL submanifold of S4, then each element of H2(W;ℤ) …