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From Homotopy to Homology through Pictures

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003251/00001

Material Information

Title: From Homotopy to Homology through Pictures
Physical Description: Book
Language: English
Creator: Khuner, Eliza A.
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2003
Publication Date: 2003

Subjects

Subjects / Keywords: Homotopy
Homology
Pictures
Mathematics
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: To construct a K(G, 1)-complex for a group G, with presentation P=< XR > one can build up skeletons by starting with a point and adding higherdimensional cells successively. It is easy to see how to attach the first two dimensions, but the third dimension and above are not clear for the general group. This paper introduces a set of tools and a series of module isomorphisms to aid in understanding the above construction. One would also like to calculate the homology groups of a group G, which is done by constructing a free resolution of ZG-modules, taking the tensor product of the modules with Z over ZG and then finding the homology groups of the resulting chain complex. This paper proves, using � among other tools � Igusa's pictures, that the map of a three cell into the 2-skeleton in the above construction is isomorphic to the kernel of the 2-dimensional map in the free resolution.
Statement of Responsibility: by Eliza A. Khuner
Thesis: Thesis (B.A.) -- New College of Florida, 2003
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Mullins, David

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2003 K4
System ID: NCFE003251:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003251/00001

Material Information

Title: From Homotopy to Homology through Pictures
Physical Description: Book
Language: English
Creator: Khuner, Eliza A.
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2003
Publication Date: 2003

Subjects

Subjects / Keywords: Homotopy
Homology
Pictures
Mathematics
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: To construct a K(G, 1)-complex for a group G, with presentation P=< XR > one can build up skeletons by starting with a point and adding higherdimensional cells successively. It is easy to see how to attach the first two dimensions, but the third dimension and above are not clear for the general group. This paper introduces a set of tools and a series of module isomorphisms to aid in understanding the above construction. One would also like to calculate the homology groups of a group G, which is done by constructing a free resolution of ZG-modules, taking the tensor product of the modules with Z over ZG and then finding the homology groups of the resulting chain complex. This paper proves, using � among other tools � Igusa's pictures, that the map of a three cell into the 2-skeleton in the above construction is isomorphic to the kernel of the 2-dimensional map in the free resolution.
Statement of Responsibility: by Eliza A. Khuner
Thesis: Thesis (B.A.) -- New College of Florida, 2003
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Mullins, David

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2003 K4
System ID: NCFE003251:00001

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