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Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups
In this paper, we redefine the torus homotopy groups of Fox and give a proof of the split exact sequence of these groups. Evaluation subgroups are defined and are related to the classical Gottlieb subgroups. With our constructions, we recover the Abe groups and prove some results of Gottlieb for the...
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Інститут математики НАН України
2005
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| Series: | Український математичний журнал |
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| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/165640 |
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irk-123456789-1656402020-02-16T01:26:23Z Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups Golasinski, M. Goncalves, D. Wong, P. Статті In this paper, we redefine the torus homotopy groups of Fox and give a proof of the split exact sequence of these groups. Evaluation subgroups are defined and are related to the classical Gottlieb subgroups. With our constructions, we recover the Abe groups and prove some results of Gottlieb for the evaluation subgroups of Fox homotopy groups. We further generalize Fox groups and define a group τ = [∑ (V×WU∗), X] in which the generalized Whitehead product of Arkowitz is again a commutator. Finally, we show that the generalized Gottlieb group lies in the center of τ, thereby improving a result of Varadarajan. Уточнено означення торових гомотопічних груп Фокса, доведено розщеплення точної послідовності цих груп. Наведено означення оціночних підгруп і знайдено їх зв'язок із класичними підгрупами Готтліба. На основі цих конструкцій встановлено деякі властивості груп Абе та доведено деякі результати Готтліба для оціночних підгруп гомотопічних груп Фокса. Наведено подальше узагальнення груп Фокса та означення групи τ = [∑ (V×WU∗), X], у якій узагальнення Арковича добутку Уайтхеда також є комутатором. Насамкінець показано, що узагальнена група Готтліба міститься у центрі групи τ, що покращує результат Варадараяна. 2005 Article Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups / M. Golasinski, D. Goncalves, P. Wong // Український математичний журнал. — 2005. — Т. 57, № 3. — С. 320–328. — Бібліогр.: 16 назв. — англ. 1027-3190 http://dspace.nbuv.gov.ua/handle/123456789/165640 515.143 en Український математичний журнал Інститут математики НАН України |
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English |
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Статті Статті |
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Статті Статті Golasinski, M. Goncalves, D. Wong, P. Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups Український математичний журнал |
| description |
In this paper, we redefine the torus homotopy groups of Fox and give a proof of the split exact sequence of these groups. Evaluation subgroups are defined and are related to the classical Gottlieb subgroups. With our constructions, we recover the Abe groups and prove some results of Gottlieb for the evaluation subgroups of Fox homotopy groups. We further generalize Fox groups and define a group τ = [∑ (V×WU∗), X] in which the generalized Whitehead product of Arkowitz is again a commutator. Finally, we show that the generalized Gottlieb group lies in the center of τ, thereby improving a result of Varadarajan. |
| format |
Article |
| author |
Golasinski, M. Goncalves, D. Wong, P. |
| author_facet |
Golasinski, M. Goncalves, D. Wong, P. |
| author_sort |
Golasinski, M. |
| title |
Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups |
| title_short |
Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups |
| title_full |
Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups |
| title_fullStr |
Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups |
| title_full_unstemmed |
Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups |
| title_sort |
generalizations of fox homotopy groups, whitehead products, and gottlieb groups |
| publisher |
Інститут математики НАН України |
| publishDate |
2005 |
| topic_facet |
Статті |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/165640 |
| citation_txt |
Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups / M. Golasinski, D. Goncalves, P. Wong // Український математичний журнал. — 2005. — Т. 57, № 3. — С. 320–328. — Бібліогр.: 16 назв. — англ. |
| series |
Український математичний журнал |
| work_keys_str_mv |
AT golasinskim generalizationsoffoxhomotopygroupswhiteheadproductsandgottliebgroups AT goncalvesd generalizationsoffoxhomotopygroupswhiteheadproductsandgottliebgroups AT wongp generalizationsoffoxhomotopygroupswhiteheadproductsandgottliebgroups |
| first_indexed |
2023-10-18T22:16:34Z |
| last_indexed |
2023-10-18T22:16:34Z |
| _version_ |
1796155093231337472 |