Timeline for Topological degree and polynomial degree
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2014 at 14:36 | history | edited | UserX2017 | CC BY-SA 3.0 |
added 11 characters in body
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| Apr 7, 2014 at 14:19 | comment | added | UserX2017 | Sorry, suppose $ H \cap \{g = 0 \} = \{0 \} $. Then consider $ L \cong \mathbb {C} \cong \mathbb {R} ^2 $. Hence, define the topological degree of $ g |_H \circ F |_L $ to be the winding number of $ g|_{H \setminus \{0 \}} \circ F |_{L \setminus \{0 \}}: L \setminus \{0 \} \to \mathbb {C} \setminus \{0 \} $ . | |
| Apr 3, 2014 at 15:30 | comment | added | Fernando Muro | @LiviuNicolaescu and AlexDegtyarev sorry I misread the question and thought he was just talking about homeomorphisms. | |
| Apr 3, 2014 at 15:03 | comment | added | Alex Degtyarev | @FernandoMuro Not any map induces a homomorphism in the homology with compact supports. As stated, the question just doesn't make sense (as the answer brlow points out). | |
| Apr 3, 2014 at 15:01 | comment | added | Liviu Nicolaescu | @ Fernando: that still requires a properness assumption. Take the constant map from a vector space to itself. It's not proper and it does not induce morphism between cohomologies with compact supports. | |
| Apr 3, 2014 at 14:46 | comment | added | Fernando Muro | @AlexDegtyarev it can be defined as the value of the automorphism induced on $2n$-dimensional cohomology with compact support (or homology with infinity support). In that dimension the aforementioned cohomology is $\mathbb Z$. | |
| Apr 3, 2014 at 12:31 | answer | added | Liviu Nicolaescu | timeline score: 5 | |
| Apr 3, 2014 at 12:18 | comment | added | Alex Degtyarev | What is the topological degree in the noncompact setting? | |
| Apr 3, 2014 at 12:08 | history | asked | UserX2017 | CC BY-SA 3.0 |