| dc.identifier.uri | http://hdl.handle.net/11401/76403 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | The first story begins with a question of Steenrod. He asked if the product in the cohomology of a triangulated space, which is associative and graded commutative, can be induced from a cochain level product satisfying the same two properties. He answered it in the negative after identifying homological obstructions among a collection of chain maps he constructed. Using later language, his construction could be said to endow the simplicial chains with an $E_\infty$-coalgebra structure. The second story also begins with a question: when is a space homotopy equivalent to a topological manifold? For dimensions greater than 4, an answer was provided by the work of Browder, Novikov, Sullivan and Wall in surgery theory, which in a later development was algebraically expressed by Ranicki as a single chain level invariant: the total surgery obstruction. After presenting the necessary parts of these stories, the goal of this work will be to express the total surgery obstruction associated to a triangulated space in terms of comodules over the $E_\infty$-coalgebra structure build by Steenrod on its chains. | |
| dcterms.available | 2017-09-20T16:50:10Z | |
| dcterms.contributor | Sullivan, Dennis | en_US |
| dcterms.contributor | Morgan, John | en_US |
| dcterms.contributor | Brumfiel, Gregory | en_US |
| dcterms.contributor | Kirillov, Alexander. | en_US |
| dcterms.creator | Medina, Anibal | |
| dcterms.dateAccepted | 2017-09-20T16:50:10Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:10Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 74 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76403 | |
| dcterms.issued | 2015-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:10Z (GMT). No. of bitstreams: 1
Medina_grad.sunysb_0771E_12473.pdf: 504041 bytes, checksum: 5f8e730525487f6c4196ea43db78cf2a (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Mathematics | |
| dcterms.subject | Algebraic surgery, E-infinity algebras, E-infinity comodules, Manifolds, Simplicial complexes | |
| dcterms.title | $E_\infty$-comodules and topological manifolds | |
| dcterms.type | Dissertation | |
